Elastomers and Components: Service Life Prediction - Progress and Challenges

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ELASTOMERS AND COMPONENTS Service Life Prediction – Progress and Challenges

Related titles: The science and technology of materials in automotive engines (ISBN-13: 978-1-85573-742-6; ISBN-10: 1-85573-742-6) Written by one of Yamaha’s leading engineers, this important book reviews each component in motor car and motorcycle engines, the materials used and the properties they need to ensure optimal engine performance. The functional requirements and properties of elastomers are discussed in detail. Materials in sports equipment (ISBN-13: 978-1-85573-599-6; ISBN-10: 1-85573-599-7) This pioneering book reviews the range of materials used in sports equipment, their requirements and the design and manufacturing issues involved in optimising their performance. It covers a wide range of sports equipment including topics such as foam protection, ball design, running shoes and sports surfaces. Permeability and other film properties of plastics and elastomers (ISBN-13: 978-1-884207-14-3; ISBN-10: 1-884207-14-6) Permeability is a critical issue in the effectiveness of elastomers as seals. This comprehensive review discusses the film properties of elastomers in relation to functions such as tear resistance, moisture absorption or barrier properties. It also reviews elastomer behaviour under differing conditions such as humidity and temperature.

Details of these and other Woodhead Publishing materials books and journals, as well as materials books from Maney Publishing, can be obtained by: • visiting our web site at www.woodheadpublishing.com • contacting Customer Services (e-mail: [email protected]; fax: +44 (0) 1223 893694; tel.: +44 (0) 1223 891358 ext.30; address: Woodhead Publishing Ltd, Abington Hall, Abington, Cambridge CB1 6AH, England) If you would like to receive information on forthcoming titles, please send your address details to: Francis Dodds (address, tel. and fax as above; email: [email protected]). Please confirm which subject areas you are interested in. Maney currently publishes 16 peer-reviewed materials science and engineering journals. For further information visit www.maney.co.uk/journals.

ELASTOMERS AND COMPONENTS Service Life Prediction – Progress and Challenges EDITED BY V.A. COVENEY

Woodhead Publishing and Maney Publishing on behalf of The Institute of Materials, Minerals & Mining

Cambridge England

Woodhead Publishing Limited and Maney Publishing Limited on behalf of The Institute of Materials, Minerals & Mining Published by Woodhead Publishing Limited, Abington Hall, Abington, Cambridge CB1 6AH, England www.woodheadpublishing.com First published 2006, Woodhead Publishing Limited © IoM Communications Ltd, 2006 The author has asserted his moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the author and the publishers cannot assume responsibility for the validity of all materials. Neither the author nor the publishers, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN-13: 978-1-84569-100-4 (book) ISBN-10: 1-84569-100-8 (book) ISBN-13: 978-1-84569-113-4 (e-book) ISBN-10: 1-84569-113-X (e-book) The publishers’ policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acid-free and elementary chlorine-free practices. Furthermore, the publishers ensure that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by Old City Publishing, Inc., USA Printed by TJ International Ltd, Padstow, Cornwall, England

Contents Series Introduction ...........................................................................................................vii Editor’s Foreword ...........................................................................................................viii Theme I – Ageing Behaviour and Life Prediction Methods for Elastomeric Materials Chapter 1.......................................................................................................................... 3 The 5-year Accelerated Ageing Project for Thermoset and Thermoplastic Elastomeric Materials: A Service Life Prediction Tool P ALBIHN Chapter 2.........................................................................................................................27 Effect of Heat Ageing on Crosslinking, Scission and Mechanical Properties AR AZURA AND AG THOMAS Chapter 3.........................................................................................................................39 Resistance of Bonds in Rubber Components to Corrosive Environments AH MUHR, M CLOTET, F DI PERSIO AND S SOLANKI Chapter 4.........................................................................................................................51 Assessment of Life Prediction Methods for Elastomeric Seals – A Review JR DALEY Chapter 5.........................................................................................................................59 Parameter Dependence of the Fatigue Life of Elastomers F ABRAHAM, T ALSHUTH AND S JERRAMS Chapter 6.........................................................................................................................75 Strain Energy Release Rates for Some Classical Rubber Test Pieces by Finite Element Analysis OH YEOH Chapter 7.........................................................................................................................91 Heuristic Approach for Approximating Energy Release Rates of Small Cracks Under Finite Strain, Multiaxial Loading WV MARS Chapter 8 .......................................................................................................................113 Abrasive Wear of Elastomers VA COVENEY AND DE JOHNSON v

Theme II – Specific Geometries and Application Issues Chapter 9.......................................................................................................................141 Life Prediction of O-rings Used to Seal Gases VA COVENEY AND R RIZK Chapter 10.....................................................................................................................153 Stress-Induced Phenomena in Elastomers, and their Influence on Design and Performance of O-Rings GJ MORGAN, RP CAMPION AND CJ DERHAM Chapter 11 .....................................................................................................................165 Magnetorheological Devices M LOKANDER AND B STENBERG Chapter 12.....................................................................................................................171 Selection of Elastomers for a Synthetic Heart Valve S BAXTER, JJC BUSFIELD AND T PEIJS Chapter 13.....................................................................................................................179 Using FEA Techniques to Predict Fatigue Failure in Elastomers JJC BUSFIELD AND WH NG Chapter 14.....................................................................................................................195 Fatigue Life Investigation in the Design Process of Metacone Rubber Springs W WU, P COOK, R LUO AND W MORTEL Chapter 15.....................................................................................................................209 Fracture of Rubber-Steel Laminated Bearings AH MUHR Appendix: Contact Details for Authors..........................................................................227 Index ...............................................................................................................................231

vi

The Rubber in Engineering Series IOM3 D Boast, JJC Busfield, VA Coveney, C Hepburn, AH Muhr, R Whear on behalf of the Rubber in Engineering Committee of the Institute of Materials, Minerals and Mining

SERIES INTRODUCTION Natural and synthetic rubber materials, or elastomers, perform essential functions in all major branches of engineering. Examples include compact, cost-effective solutions in: sealing; traction and transmission; shock, vibration and noise control. The difference between an appropriate and an inappropriate match of the material and design of an elastomer-based component to the application is often the difference between success and failure overall. Some notable aspects of the behaviour of model elastomeric materials became understood some 70 years ago. In contrast, the use of practical materials in real applications continues to pose many fundamental questions for research as well as more application-specific questions for research and development. The objective of the Rubber in Engineering Series is to keep the reader abreast of the progress made by specialists working in the field and aware of challenges remaining in engineering sectors such as: automotive, aerospace and bioengineering.

vii

Editor’s Foreword VA Coveney

An elastomeric component may be said to reach the end of its life when it fails to function properly – as in seal leakage or a loose elastomeric bushing – or when its appearance or some other aspect of its behaviour leads to failure of an inspection. Either way, longer more assured lives are being expected of rubber components at the same time as other demands – such as: reduced space and increased operating temperature. This volume Elastomers and Components: Service Life Prediction Progress and Challenges had its beginnings in a conference organised by the Rubber in Engineering Committee of the Institute of Materials, Minerals and Mining. About two-thirds of the contributions herein originate from the conference, the remainder are from other experts around the world. All contributions have undergone thorough anonymous peer review and updating on content and clarity. In the first part of this volume, the emphasis is on the current state of knowledge in various types of ageing behaviour of elastomeric materials and on current methods of service life prediction. In the second part of the volume the focus shifts to specific geometries and application issues.

THEME I – AGEING BEHAVIOUR AND LIFE PREDICTION METHODS FOR ELASTOMERIC MATERIALS Although there are other types of ageing and damage, thermo-oxidative effects are often crucial. In chapter 1 of theme I, Albihn focuses principally but not exclusively on thermo-oxidative ageing. Albihn explains the Arrhenius method and its potential limitations and describes experiments to apply and test the method over periods of up to 5 years at modestly elevated temperatures for a very wide range of elastomeric materials and for a number of test procedures. The effects of immersion in water are also considered. The set of materials data described offers an invaluable tool for designers and researchers alike. However, Albihn also points out that an understanding of mode of component-specific failure is required to complement the materials (property, temperature, time) data (see theme II). It is only then that it can be judged what material property (or properties) and what failure criterion (or criteria) should be selected. As indicated by Albihn a major problem in life prediction can be the presence of more than one ageing mechanism. In chapter 2, Azura & Thomas use Tobolsky’s two-network theory to quantify different ageing mechanisms (continued crosslinking, scission of crosslinks, scission of polymer chains) and examine the effect on strength and fatigue viii

properties in natural rubber. In doing so they also introduce the strain energy release “rate” (SERR or tearing energy, T or G) approach to crack growth prediction in elastomers (see below). Their work quantifies differences between natural rubber vulcanized with “conventional” (sulphur rich) and “efficient” systems. Although crosslinking and scission effects in the elastomer are often the cause of failure this is not always the case. For example, elastomer components very often include bonds to a more rigid material; such bonds can be a weak point in the system. Muhr et al (chapter 3) examine possible mechanisms for bond failures in saline conditions. They conclude that in such circumstances electrochemical effects are often to blame. Their findings are of practical and theoretical interest. In chapter 4 Daley reviews the range of methods used in the life prediction of seals. The wide range of causes that can bring about the end of useful life of even a static O-ring is indicated. The complexity means that, although much progress has been made, fully comprehensive models (in finite element analysis for example) remain to be developed. In some cases the mode of failure of an elastomer component is by cracks driven by mechanical stress rather than environmental factors. For fatigue, a stress-life (“S-N” or Wöhler curve) approach is often used but can give widely inaccurate predictions; the SERR (T) approach – sometimes referred to, in elastomers science, as the energetics or the fracture mechanics approach - is an alternative (Busfield et al, 1999; Azura & Thomas, 2005; Yeoh, 2005; Mars, 2005; Coveney & Johnson, 2005; Baxter et al, 2005; Busfield & Ng, 2005; Muhr, 2005). T is defined, for a testpiece or component with the external boundaries fixed, as the decrease of elastic energy stored energy per unit increase of crack area. The key premise of the SERR approach is that the rate of increase in length of a crack with time (dc/dt) or fatigue cycle number (dc/dn) is a geometry-independent function of T. It is well known that for natural rubber materials when a testpiece or component is subjected to force or deformation cycling under non relaxing conditions, counter-intuitive results can be obtained for crack growth rate and fatigue life – one of several complications in fatigue crack growth. Specifically, if R is defined as the ratio of minimum (cyclic) strain energy release rate (Tmin) to the maximum (Tmax), for a given Tmax, life can increase strongly for increasing R (Lake & Thomas, 1988). Indeed, fatigue life can sometimes increase for a natural rubber testpiece or component if the maximum load during cycling is increased provided that the minimum load is also increased. Such effects are normally ascribed to the tendency of natural rubber to crystallise when highly strained. In chapter 5, Abraham et al report fatigue experiments on non strain-crystallising elastomers filled with carbon black (nm-µm scale particles of carbon). They find that with filled non-crystallising materials, too, increasing the minimum load can lead to dramatic increases in fatigue life. They find no such noticeable effects for unfilled non-crystallising materials. Interestingly, for their experiments Abraham et al find maximum stored energy to be a good indicator of fatigue life. Abraham et al also report on cyclic softening of filled EPDM: there was a continuous decrease in “modulus” (E*) with cycle number (n). For much of the life the plot of E* against log n is approximately linear. In order for the SERR (T or G) approach to fatigue crack growth to be used, crack growth data must be correctly interpreted. In chapter 6, Yeoh uses the finite element (FE) method to evaluate T or G for various geometries (of testpiece/component and crack) and compares the results with standard formulae in the literature. Insight is ix

thereby gained into the likely behaviour of cracks. In addition Yeoh comments on practical issues of FE modelling in the context of crack growth prediction in elastomers. Although the SERR approach (especially, coupled with finite element analysis, FEA) provides a workable method of prediction of crack growth it does have limitations. One complication concerns the effects of non-relaxing conditions (R ≠ 0 – see above). A second potential difficulty concerns three-dimensional aspects of crack behaviour (Charrier et al, 2003; Harris, 2003). A third difficulty concerns the fact that it is not always clear where fatigue cracks are likely to first appear; straightforward use of the SERR approach within finite element analysis could be prohibitively intensive computationally in such cases. Mars (in chapter 7) addresses the third of the above difficulties by putting forward a possible SERR-based field (cracking energy density, CED) approach for predicting the timing and position of early crack growth within a rubber component. An underlying assumption here is the uniform distribution of pre-existing flaws. Mars’ comment that crack closure remains an issue to be addressed applies not just to the CED method but more generally to modelling of crack growth in elastomers. As stated above, sometimes more than one “fundamental” ageing mechanism acts at the same time. Sometimes, too, it is still not clear which fundamental mechanisms are acting: ironically this is the case for abrasive (rubbing) wear of elastomers. In chapter 8, Coveney & Johnson review attempts to explain the phenomenon and present new data which sheds light on some issues relating to abrasion but also poses further questions. Specifically it is found that existing SERR-based approaches are capable of accounting for some but not all aspects of behaviour.

THEME II – SPECIFIC GEOMETRIES AND APPLICATION ISSUES In the first of the chapters on theme II (chapter 9), Coveney & Rizk report work which reemphasises that the mode of failure of an O-ring seal - and so which are the most important ageing mechanisms – depend strongly on details of the conditions and the application. Elaborations of the Arrhenius method are also referred to. The emphasis of chapter 10 by Morgan et al is on the use of elastomeric seals in extreme environments – downhole in an oil well for example. They point out that applied stress can accelerate changes of material property with time. Morgan et al also discuss explosive decompression and the role that moulding memory effects may play. There is a growing interest in smart materials in engineering applications. Magnetorheological elastomers are one class of such material. In chapter 11, Lokander & Stenberg explain some of the basic features and advantages of magnetorheological elastomers but go on to flag ageing in such materials as a potentially serious issue which is the subject of ongoing research. Polymers used in human implants must exhibit two-way compatibility – lack of toxicity and ability to withstand the biological environment are both essential; synthetic heart valves must, moreover, exhibit good fatigue resistance in that environment. In chapter 12, Baxter et al use a SERR (T or G) approach in part of the selection process for candidate materials for such valves. In chapter 13, Busfield and Ng show how the SERR crack growth prediction method may be used within the finite element method. Using a real example component they report that the method can give results in acceptable agreement with observed behaviour. They also highlight future challenges including: multiple cracks, instability in finite element modelling and strain induced material anisotropy. x

Wu et al report, in chapter 14, a case-study involving the design for fatigue life of a large rubber-metal spring. Simple rule-based design methods were found to be inadequate but a more sophisticated (field-based) approach using the finite element method and testpiece fatigue data gave satisfactory results. In the final chapter, Muhr examines approaches to design for fatigue life of laminated rubber-steel bearings. He reminds the reader that whereas in some applications the early stages of crack appearance/growth are the main focus, in others late stage crack growth is more important. He concludes that the SERR approach can give useful results for late stage crack growth but points to some remaining puzzles and challenges with regard to non-relaxing fatigue and early-stage fatigue in the presence of high stress concentrations.

REFERENCES Azura AR & Thomas AG (2005) “Effect of heat ageing on crosslinking, scission and mechanical properties” (This Volume). Baxter S, Busfield JJC & Peijs T (2005) “Selection of elastomers for a synthetic heart valve” (This Volume). Busfield JJC & Ng WH (2005) “Using FEA techniques to predict fatigue failure in elastomers” (This Volume). Busfield JJC, Ratsimba CHH & Thomas AG (1999) “Crack growth and prediciting failure under complex loading in filled elastomers” in Finite Element Analysis of Elastomers D Boast & VA Coveney (eds), Professional Engineering Publications, Bury-StEdmunds, 235-250. Charrier P, Ostoja-Kuczyushi, Verner E, Marchmann G, Gornet L & Chagnar G (2003) “Theoretical and Numerical Limitations for the Simulation of Crack Propagation in Natural Rubber Components” in Constitutive Models for Rubber III JJC Bushfield & AH Muhr (eds), AA Balkema. Coveney VA & Johnson DE (2005) “Abrasive wear of elastomers” (This Volume). Gent AN (1994) “Strength of elastomers” chapter 10 in Science and Technology of Rubber JE Mark, B Erman & FR Eirich (eds), Academic Press, London, 471-512. Harris JA (2003) “Critical tearing energy as a criterion for failure of elastomeric components” Fracture of Polymers, Polymer Physics Group of the Institute of Physics, Rubber in Engineering Committee of the Institute of Materials, Minerals & Mining; Queen Mary, University of London, 8 Jan. Lake G & Thomas AG (1988) “Strength properties of rubber “ in Natural Rubber Science and Technology AD Roberts (ed), Oxford Science Publications. Mars WV (2005) “Heuristic approach for approximating energy release rates of small cracks under finite strain, multiaxial loading” (This Volume). Muhr AH (2005) “Fracture of rubber-steel laminated bearings” (This Volume). Yeoh OH (2005) “Strain energy release rates for some classical rubber test pieces by finite element analysis” (This Volume).

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CHAPTER 1

The 5-year Accelerated Ageing Project for Thermoset and Thermoplastic Elastomeric Materials: A Service Life Prediction Tool P Albihn The Swedish Institute for Fibre & Polymer Research (IFP Research AB) Mölndal, Sweden

SYNOPSIS A large long-term accelerated test programme for elastomers (rubbery materials) is reported. In the programme the effects, on a range of physical properties, of accelerated ageing in a variety of environments for periods up to five years were studied for 48 thermoset rubbery materials and 27 thermoplastic materials. Example results for thermoset rubbery materials are given here. The main focus is on thermo-oxidative ageing although the, sometimes very significant, effects of other factors is also considered. Key findings include the following [(a)-(c)]. (a) The wide validity of the (log time to failure against reciprocal absolute temperature) Arrhenius extrapolation method is confirmed. (b) The results re-emphasise the importance of carefully specifying ageing conditions (e.g. which fluids there will be exposure to). The suitability ranking of two different elastomeric materials is often reversed if the conditions are changed. (c) Ageing causes some measures of material properties to decrease more rapidly than others – indeed, some increase rather than decrease. Moreover, the slopes of the Arrhenius plots for (values of) different material properties can differ markedly. Selection of failure criteria is therefore crucial for lifespan prediction; thus it needs to be known which physical properties are important and what range of values of those properties is acceptable for a given application.

1 INTRODUCTION Rubbery materials, or elastomers, are often used in demanding environments and in components with high reliability requirements even over long periods in use. Operational lives of 10 years and more are not unusual. This has increased the importance of having access to adequate material data and of having methods for service life prediction. 3

4

Elastomers and Components: Service Life Prediction – Progress and Challenges

In practice, it is generally impossible (from a time or cost viewpoint) to perform laboratory testing of the ageing properties of a material for times approaching the lives of rubbery materials in service. Manufacturers and/or users of elastomers usually have to do short-term accelerated tests and thereafter, on more or less well justified grounds, have to make a judgement on the suitability of the material. Correspondingly, most specification sheets and data in the literature relating to the ageing of rubbery materials refer to short-term (accelerated) tests of a few days or weeks. As a basis for the choice of materials for components subjected to long-term use, these data are not sufficient; and more time-consuming testing is usually necessary. The reason for this is that a non-negligible error arises when results are extrapolated from inappropriately high testing temperatures to normal operating temperatures. A rough guide is that a temperature increase of ten degrees increases the reaction rate by a factor of 2-3. However, extrapolation is not recommended in cases where the test temperature is more than 20-30°C above the operational temperature range, i.e. a four to eight fold acceleration. During the last 20 years, IFP Research (The Swedish Institute for Fibre & Polymer Research) has, within the Rubber sub-programme, worked on testing different rubbery materials – both standard materials and special materials – for test periods that greatly exceed what is normal. The work has enabled the Arrhenius plot method (see below) to be comprehensively checked for a wide range of materials and has, moreover, resulted in extensive test data which is only modestly accelerated. All data from the series of long duration tests performed at IFP Research have been compiled into a handbook (Andersson, 1999). The purpose of the endeavour is to provide an aid for designers, using thermoset elastomers (rubbery materials) and thermoplastic elastomeric (TPE) materials, who are interested in the lifetime prediction of the material and components. Questions such as: “How long will this rubber component last?”, “Can I increase the operation temperature by 10°C and still achieve the requirement of a service life of 20 years?” or “One of my customers has had a failure of one of our rubber components after only 2 years use, what is this due to?” can be answered with the help of the (long duration test) study. A partial goal is to explain in simple terms the concept of lifetime prediction for designers and rubber users. Another is to equip rubber technologists and designers with as complete a database as possible with regard to the lifespan of different thermoset and TPE material types. All in all, measurements were made on 48 thermoset elastomeric materials (from 21 polymer types) and 27 thermoplastic elastomeric materials (from 11 polymer types); for these materials 1-8 properties were tested over periods lasting from 1 to 5 years (43800 hours). Generally the materials were aged in an unloaded state and in three different environments: hot air, hot water and hot oil. And generally the following measures of properties were evaluated: hardness, elongation at break, tensile strength and tensile stress at 100% elongation. For some materials, compression set, tension set, relaxation in compression and relaxation in tension were also investigated. The ageing took place at several different temperatures and Arrhenius plots (lifespan diagrams) were produced for all materials. The complete material formulation and initial material property details are given by Andersson (1999). No other investigation involving accelerated ageing times as long as 5 years has, to our knowledge, previously been reported. Moreover, recently RAPRA has published a report reviewing the main theories and test methods for ageing of rubber and giving a large number of abstracts (Brown et al, 2000). Furthermore, RAPRA has also recently produced an extensive report on natural ageing (Brown & Butler 2000). The RAPRA reports complement the programme reported here. It is now possible to verify in many ways the theories and methods of accelerated ageing. The results of

Accelerated Ageing Project

5

accelerated ageing on several materials, methods, properties and environments can be found in the Andersson (1999) handbook and without waiting 40 years they can be compared with natural ageing (Brown & Butler, 2000). Correctly used, the output of the IFP Research study (Andersson, 1999) is a powerful aid in the estimation of the lifetime of a rubber material or a thermoplastic elastomer. In the present chapter I shall summarise some of the findings of IFP Research’s 20 year study (Andersson, 1999) and also refer to other relevant studies.

2 LIFESPAN: SOME IMPORTANT FACTORS TO CONSIDER What influences the service life of a rubbery material? A material has a number of properties such as tensile strength, elongation at break, hardness, compression set, chemical resistance, colour and glass transition temperature. Ageing can be defined as the changes in these properties, decrease or increase, which take place with time. What causes the ageing of an elastomer? There are many environmental factors that can cause degradation of the material and its performance: oxidative degradation, UV-light, moisture, temperature, fluids, ozone, micro-organisms. Mechanical factors such as changing stresses and abrasion may also contribute to or constitute ageing. In order to predict the behaviour of the material in service and the effect on the component, such factors may have to taken into account. In this chapter, though, the main focus will be on thermo-oxidative ageing, although for some test methods the behaviour may depend on other types of chemical or physical processes. In testing for ageing the most important factors are: (a) (b) (c) (d) (e)

type of elastomeric material temperature testing environment property measured and test method mechanical stress (if any)

The original value of the property and its dependence on time (e.g. increasing or decreasing) can vary depending on how (a)-(e) are chosen. Different materials can be compared according to any of the following or other properties or conditions: -

hardness, tensile strength, elongation at break, compression set, temperature in use, in air, oils or water.

It is important to remember that service life can be a relative concept. Depending on specific requirements, one, two or several of the above-mentioned properties can be measured to evaluate the service life of the component. Because of specific requirements for different components – such as different materials, different uses and different lengths of service life – the quantitative criteria can vary greatly. It is extremely important in service life

6


prediction to consider carefully, and at an early stage, which property or properties one considers to be critical for the component. In the same way, it is very important at an early stage to fix the lower limit for what is to be considered acceptable (e.g. a 50% decrease in the tensile strength). The result of these two decisions has a profound influence on the estimated service life of the product. Following considerations of the type described, a number of suitable material can be selected for further evaluation. In Andersson (1999) a ranking order of tested materials for each property evaluated is presented. This simplifies the problem of comparing different materials and that of finding relevant and comparable data.

3 THE ARRHENIUS EQUATION The rate constant k in a chemical reaction is, in general, a function of the absolute temperature. The most common model used in ageing predictions is the Arrhenius equation:

(1) The quantities Ea1 and Ea2 are the activation energy in units of Joules per mole and Joules respectively; R is the universal gas constant and kB the Boltzmann constant; b is a measure both of the interaction frequency and of the probability that the reaction will occur. The activation energy is constant as long as the reaction mechanism remains unchanged. Also, the parameter b can be considered to be constant if the temperature range investigated is not too large. In practice, k can thus be said to be a measure of the rate of change of a property with respect to time. When the temperature is raised, the rate of a chemical reaction generally increases. For many reactions in organic chemistry, a ten-degree (C or K) temperature increase gives a 2-3-fold increase in reaction rate. The Arrhenius equation is used to produce an Arrhenius diagram. After integration and taking logarithms, Equation (1) leads to:

(2) Here B corresponds to a particular value of a material property. A graphical presentation of Equation (2) with ln (t) plotted against the reciprocal temperature 1/T (with B held constant) results in a straight line with slope Ea1/R and is called an Arrhenius diagram. In general, Arrhenius diagrams (or plots) have been found to be valid in describing the ageing of most organic materials. Using this relationship, data obtained at one time or at one temperature can thus be extrapolated to another time or another temperature. An example will now be given of how to construct and use an Arrhenius diagram. The dependence of a property (here tensile strength) on exposure time at various temperatures is shown for an example material in Table 1 and in Figure 1. A certain level (e.g. 50% reduction) of the property is chosen as the criterion for end of service life. Using computer generated curves fitted by eye to the property-time data (Figure 1) an Arrhenius diagram is then constructed as shown in Figure 2.


7

Table 1 Percentage of initial tensile strength (15.8 MPa) shown as a function of exposure time at stated temperature. For a natural rubber (NR2, formulation see Table 3). Tensile strength measurements were performed according to ISO 37 (1994).

The availability of a property-time diagram means that the service life criterion can be chosen freely according to the demands imposed by the expected area of use. As indicated above, the slope of the straight line in an Arrhenius diagram is a measure of the activation energy of the dominant reaction in the ageing process. Extrapolation of the straight line means that a material’s ageing behaviour at one temperature can be determined by performing tests at a higher temperature over a considerably shorter period. However, one must be on guard

120 100

q (°C)

80

55 70 85 100

TSN 60 40 20 0 0.01

0.1

1

10 t (days)

100

1000

10000

Fig. 1 Percentage of initial tensile strength (TSN) shown as a function of exposure time (t) at various temperatures. The material is a natural rubber (NR2, Table 3). Tensile strength measurements were performed according to ISO 37 (1994).

8

Elastomers and Components: Service Life Prediction – Progress and Challenges 10000 1000

t0.5 (days)

100 10 1 0.1 3.30 20

3.10 50

2.90

2.70 100

2.50

2.30 150

1000/T (K–1)

2.10

1.90

200

250 q (°C)

Fig. 2 Arrhenius plot for NR (NR2, Table 3) aged in air. Time to reduction of tensile strength to 50% of initial value (t0.5) against reciprocal temperature.

against factors that can lead to an incorrect estimate. One such factor is the possibility that the ageing reaction, which predominates at the test temperature, gradually gives way to another reaction at another temperature. Because of this, extrapolation is not generally recommended in cases where the (accelerated test) temperature exceeds the application temperature by more than 20-30°C – i.e. an acceleration factor of more than 4 to 8. Of course larger extrapolations can be made provided one is aware of the risks. In the example presented here, following the 30°C rule one could almost extrapolate down to room temperature. At about 30°C, the material is expected to last 10 000 days: about 27 years. As indicated above, different criteria can be used to estimate lifespan. In material tests not specific to any particular application, a common criterion is defined as reduction of a material property to 50% of the original value (for e.g. tensile strength and elongation at break). In measurements of compression set on aged materials, other levels are usually chosen, e.g. 70 or 80%. Requirements on absolute values can also be made, such as a maximum allowable value of a certain property (e.g. 90 IRHD for hardness). To answer definitively the question of whether or not the material will perform satisfactorily in a particular application for 20 years at a particular continuous operating temperature, an absolute (material) requirement (or set of requirements) appropriate to the application must be defined. Of course to define suitable material requirements with confidence one must understand quantitatively how a component fails or becomes unserviceable. Such issues are principally dealt with elsewhere in this volume. Thus an Arrhenius diagram can be used to assist practical design work with regard to: material selection; determination of test condition (time and temperature); and (subject to caveats given above) lifespan estimation. Arrhenius diagrams are used in the evaluation of the ageing behaviour of polymeric materials in many standards e.g. ISO 11346 (1997), IEC 216, ASTM D 3045 (1997) and UL-746 B (1979). The foregoing standards describe ageing in air. Similar testing can be carried out in


9

other media. A warning must however be issued regarding ageing in other media since it is often oxygen which is the primary cause of ageing (thermo-oxidative degredation) – so the ageing medium must be well characterised with respect to its oxygen concentration. A related complicating factor is that testpieces generally have quite small dimensions whereas the dimensions of rubber components vary widely, and hence the balance between oxidative and non oxidative effects may vary greatly (see Barnard & Lewis, 1998, for example). In the study reported here (Andersson, 1999) the testpieces for the chosen property tests were generally kept unloaded (i.e. force-free) at different temperatures. The change in a property value (at room temperature) was recorded and compared with the unaged value.

4 EXPERIMENTAL 4.1 MATERIALS

All in all, 75 materials were tested – 48 thermoset rubbery materials (from 21 polymer types) and 27 thermoplastic elastomers (from 11 polymer types) – see Table 2. The materials ranged from common commercial materials to rarer more specialised materials and were chosen to cover the full spectrum of possible material types and variants. For some polymer types only one material was tested, for other polymer types up to six materials were tested; these materials could have different manufacturers, different additives, different vulcanising agents etc. The materials were, moreover, characterised to various extents. For some materials only one property was measured, whilst in others up to eight properties were measured. Compositions and (unaged) properties of example materials are shown in Table 3. Testpieces were manufactured by compression moulding or injection moulding. The thermoset rubber materials were mainly compression moulded, whereas the thermoplastic elastomers were all injection moulded. The most common testpiece geometry was the dumbbell (Figure 3). 4.2 METHODS TENSILE STRENGTH AND ELONGATION AT BREAK

Tensile strength and elongation at break were measured according to ISO 37 (1994) for all materials. For air-aged testpieces, the tensile stress at an elongation of 100% was also measured. HARDNESS

The hardness of the rubber materials (IRHD) was determined according to ISO 48 (1994) on all testpieces. COMPRESSION SET (25%)

The compression set was determined according to ISO 815 (1991) with a small testpiece (type B, diameter 13 mm, thickness 6.3 mm). TENSION SET (50%)

The tension set was determined according ISO 2285 (1995), method 2 (constant elongation).

10


Table 2 List of polymer types tested. (Superscript “T” indicates a thermoplastic elastomer.) (Tradename in parenthesismaterial quality is no longer commercially available.)

Polymer type

Trade name

1 2

Acrylic rubber (ACM) Butadiene styrene elastomerT (SBS)

3 4 5

Butyl rubber (IIR) Chlorinated polyethylene elastomerT (CPE) Chloroprene rubber (CR)

6 7 8 9 10

Chlorosulphonated polyethylene rubber (CSM) Epichlorohydrin rubber (ECO) Ethylene acrylate rubber (EACM) Ethylene propylene diene rubber (EPDM) Ethylene propylene diene rubber/PolypropyleneT (EPDM+PP)

11 12

Ethylene propylene rubber (EPM) Ethylene vinylacetate copolymerT (EVA)

13

Fluorinated rubber (FPM)

14 15 16

Fluorosilicone rubber (MFQ) Hydrogenated nitrile rubber (HNBR) Natural rubber (NR) [e.g. SMR 5 CV: Standard Malaysian Rubber with a Mooney viscosity of 5.] Nitrile rubber [acrylonitrile (ACN)butadiene, NBR]

Hycar 4021 Kraton 3226 Kraton TOB 5152 (Solprene 416) Esso Butyl 268 CPE 4213 Neoprene WB Neoprene WRT Hypalon Herclor C Vamac B 124 Vistalon 4608 (Levaflex EP-370) Santoprene 103-40 Santoprene 101-73 EPM Dutral (Evathene 28-05) (Alkathene VJG 501) Viton GH Viton E60 Silastic LS 63 Zetpol 2000 L SMR 5 CV

17 18

Olefinic block copolymerT (TOE)

19 20 21

25

Perfluorocarbon rubber (FFKM) Polynorbornene rubber (PNR) Polyvinyl chloride (highly plasticised) elastomerT (PVC) Propylene oxide rubber (GPO) Silicone rubber (Q) Styrene butadiene rubber (SBR) [e.g. SBR 1500 is SBR with an average molecular weight of 1500] Styrene ethylene butylene elastomerT (SEBS)

26 27

Tetrafluoro ethylene propylene rubber (FEPM) Thermoplastic copolyester elastomerT (PEEA)

28 29 30

Thermoplastic ester ether elastomerT (TPAE) Thermoplastic natural rubberT (TPNR) Thermoplastic polyurethaneT (TPU)

31 32

Urethane rubber (AU) Urethane rubber (EU)

22 23 24

22 ACN 50 Mooney 33 ACN 50 Mooney 45 ACN 50 Mooney TPR 1622 TPR 1692 TPR 078 Dutral TP 30/X Uneprene 690 Kalrez Norsorex (Pevikon S-687)

Manufacturer Goodrich Shell Shell Phillips Esso Dow DuPont DuPont DuPont Hercules DuPont Exxon Bayer Monsanto Monsanto Montedison ICI ICI DuPont DuPont Dow Zeon

Uniroyal Uniroyal Uniroyal Montedison ISR DuPont CdF Kema Nord

Parel 58 Wacker 700 1500 1503

Zeon Wacker

Kraton G7720 Kraton G7820 Elaxar 8431Z Aflas 150 Pebax 2533 SNOO Pebax 3533 SNOO Hytrel 4056 TPNR 7525/10 Desmopan PU 1517 Elastollan P 85 A Elastollan C 83 A Vulkollan 25 Adiprene L 42

Shell Shell Shell Ashai Glass Ato Chimie Ato Chimie DuPont MRPRA Bayer BASFElastogran BASF Elastogran Bayer Uniroyal


11

Table 3 Examples of (a) material formulations [proportions by mass of ingredients and cure conditions], (b) cure characteristics, (c) reference test results (unaged testpieces).[For key to polymer abbreviations see Table 2.]

Polymer and Material identification Number: (a) Formulation and cure conditions Units Vulcanisation duration and temperature min/ ºC Post-cure duration and temperature hour/ ºC NR (SMR 5 CV) EPDM Vistalon 4608 FPM Viton E 60 C Carbon black filler N 550 (FEF) Carbon black filler N 990 (MT) Oil, aniline point 45°C, kinematic viscosity 900 mm2/s, flash point 40°C Oil, aniline point 100°C, kinematic viscosity 33 mm2/s, flash point 40°C Zinc oxide Stearic acid Antioxidant, TMQ (poly-2, 2, 4-trimethyl-1, 2-dihydroquinoline) Flectol Flakes Magnesium oxide Zinc stearate Sulphur (95% S + 5% Oil) CBS (N-cyclohexylbenzothiazole2-sulphenamide) Peroxide Perkadox 14/40 (b) Cure characteristics Mooney 125°C, ML min value Mooney 125°C, ML t5 Rheometer (Monsanto 100) 190°C, 3º, min value Rheometer 190°C, 3º, t2 Rheometer 190°C, 3º, t90 Rheometer 190°C, 3º, max value (c) Reference test results (unaged testpieces) Hardness Hardness Tensile stress (force divided by original crosssectional area) at 100% elongation Tensile strength (maximum tensile stress before break) Elongation at break

NR2

EPDM24

FPM37

15/160

15/160 3/150

15/160 23/230

100 100 100 75

55 10

30

5 1

20 5 1

2

2 3 6

2.75 1.5 10

M-units minutes R-units

41.0 19.1 13.93

55 24 16.39

29.4 >24 10.42

minutes minutes R-units

0.93 1.82 70.2

0.72 3.68 77.84

2.55 3.71 110.62

º Shore A IRHD MPa

64 64 2.5

61 60 1.4

57 59 1.1

MPa

15.8

11.4

7.1

%

420

400

410

Fig. 3 Dumbbell testpiece geometry [ISO 37 (1994) testpiece no 1, overall length 115 mm, gauge length 33 mm, width of central section 6 mm, thickness 2 mm].

12


Fig. 4 Ageing of testpieces in a hot-air oven.

RELAXATION IN COMPRESSION (25%)

Relaxation in compression was determined according to ISO 3384 (1991), method A (all force measurements carried out at the testing temperature). Testpiece as for compression set. STRESS RELAXATION (50%)

Stress relaxation, in tension, was determined according to ISO 6914 (1985), method A (constant elongation). AGEING IN AIR

The ageing in air was carried out according to what is now ISO 188 (1982) at temperatures of + 40, 55, 70, 85, 125, 150, 175, 200, 225 and 250°C in a hot air oven (Figure 4). SWELLING

During ageing in water and oil, swelling (change in volume) of the testpieces was measured. AGEING IN WATER

The ageing in water was carried out according to ISO 1817 (1985). It was performed in tap water at 95°C (and normal pressure) and in an autoclave at a temperature of 125°C. During the test at 95°C, water lost due to evaporation was replaced continuously and all water was changed completely each time samples were taken out to be tested. During


13

the test at 125°C, in a sealed autoclave, only the water lost during removal of samples for testing was replaced. AGEING IN OIL

The testing took place according to ISO 1817 (1985). In all, three oils were used in the test series: oils number 1 and 3, and oil number 1 (oxidised). REPEATABILITY

The repeatability in all tests was normally to within ± 1.5 IRHD for the hardness testing and within ± 10% of the measured values for the testing of elongation at break, tensile strength and tensile stress at an elongation of 100 mm. SAMPLING INTERVALS

In the 5-year tests the materials were tested after 1 and 3 days, 1, 2, 4, 8, 16 and 32 weeks, 1.25, 2.5 and 5 years of ageing. In the 1-year tests the materials were tested after 1, 2, 4, 7, 14, 28, 56, 112, 224 and 365 days of ageing. A test sequence was ended when the property value fell outside a pre-determined range, depending on the test method, or when the maximum duration of the test was exceeded. LIFESPAN CRITERIA

Lifespan criteria indicate the value which a certain measured property may attain before the material is considered to be unserviceable. In this study, criteria have been chosen with the aim of arranging lifespan diagrams for as many of the investigated materials as possible. Often, the criterion of a 50% decrease in the level of a material property has been used. For ageing in water and oil, only one temperature was used and it is consequently not possible to construct an Arrhenius plot. Consequently, the time to a 50% reduction has been used as a yardstick of the ageing resistance of the material in water and in oil. In the analysis of the results from relaxation in compression – where, again, only one temperature was used – the time to a 50% reduction of force has been used as an indication of the ageing resistance of the material.

5 RESULTS AND DISCUSSION To show the ageing data collected, a series of diagrams on one material – a natural rubber, NR2 (Table 3) – are presented and commented upon. NR2 was tested for the effects of time and temperature on many properties. In Figure 5 the NR2 data for elongation at break are presented. In Figure 5 and in similar plots in Andersson (1999) actual data points are presented to enable the user to draw their own conclusions as to how an ageing curve is to be drawn. Each point is the average of all measurements at that time and temperature, but error bars are not used due to the large amount of data. In Figure 5 there is limited scatter and a good picture of the ageing of the material is given. Elongation at break (EB) is often quite a useful property with which to evaluate the material. Higher temperatures – and particularly those in excess of 100°C – decrease the service life, and lead to rapid embrittlement of natural rubber, making both testing and interpretation of test results more difficult. In the example given here, one EB value (at 150°C) is actually higher than for the unaged material but this is probably due to heavy degradation. However a service life of a day or

14

Elastomers and Components: Service Life Prediction – Progress and Challenges 140 q (°C)

120

40 55

100

70 80

85

EBN

100

60

125 40

150 175

20 0 0.1

200 1

10

100

1000

10000

t (days) Fig. 5 Elongation at break (normalised by the value for the unaged material and expressed as a percentage, EBN) of NR2 (Table 3) against duration of ageing (t) in hot air at stated temperatures (θ).

two is seldom of great interest. If the requirement is for a continuous exposure to 70°C, the EB falls to 50% of its initial elongation at break in about 50 days. Tensile strength (TS) can also be used to evaluate ageing performance; often, though, TS decreases more slowly than EB. This is illustrated in Figure 6 where the 50% reduction of the original tensile value takes about 100 days at 70°C. In contrast to the behaviour for EB, and despite some scatter, the time for TS to fall to 50% of its initial value appears to decrease wholly monotonically with ageing temperature. The differences in ageing characteristics for EB and TS emphasise the importance of deciding on the most important material property (or properties) for life prediction in a given application, as well as deciding on the acceptable range of values for that property (or properties). Ageing of rubber is usually associated with an increase in hardness (Figure 7). However as a measure of ageing this property is less widely used, as the change usually is less and is more difficult to evaluate than EB or TS. The question of what change in material hardness corresponds to the end of the useful life can depend strongly on the application. Stress relaxation (the decrease, with time, of force exerted by a component or testpiece subjected to a constant deformation) and the very closely related phenomenon of creep (change of deformation for constant load) are both important aspects of behaviour in ageing (Figure 8). Set (the proportion of deformation which is not recovered, after a certain interval, following stress relaxation) is also related. Unaged fully rubbery material has a compression set close to zero. High temperature compression set is also widely used as an indication of how well a rubber testpiece has been vulcanised. During the compression set test a squat cylinder of the material is compressed so that part of the surface is in direct contact with metal, limiting the exposure to oxygen. Example results are shown in Figure 9. Compression set is often used as one indication of expected life in sealing applications.


15

120 q (°C)

100

40 80

55 70

TSN 60

85 100

40

125 20 0 0.1

150 1

10

100

1000

10000

t (days) Fig. 6 Tensile strength (normalised by the value for the unaged material and expressed as a percentage, TSN) of NR2 (Table 3) against duration (t) of ageing in hot air at stated temperatures (θ ).

q (°C)

160

40 140

55 70

120

85 HN 100

100 125

80

150 60 40 0.1

175 200 1

10

100

1000

10000

t (days) Fig. 7 Hardness (IRHS, normalised by the value for the unaged material and expressed as a percentage, HN) of NR2 (Table 3) against duration (t) of ageing in hot air at stated temperatures (θ).

Practical experience indicates that a compression set value of up to 80% can be used as a criterion when evaluating material for sealing applications. For NR2 at 70°C the service life suggested by using a criterion of 80% compression set would be about 60 days (Figure 9); in contrast, a criterion of 50% compression set would give a service life of only 10 days at 70°C.

16


Fig. 8 Stress relaxation (at 50% extension) for NR2 (Table 3). Force (F) against duration of ageing (t) hours in hot air at 70°C. ISO 6914. Test piece thickness 1 mm, width 4 mm, length 80 mm. Triplicate test.

The force remaining in a material to keep a seal functioning can be evaluated using relaxation in compression where the decay of the force with time is measured. An example is given in Figure 10. The test shown here was carried out at 100°C. Using a criterion of 30% force remaining, the service life would be about 10 days at 100°C. However a direct comparison with the results of the compression set method in Figure 9 is complicated because of the nonlinear viscoelastic behaviour of the material.

100

80

q (°C) 55

60

70

CS

85

40

100 20

0 0.1

1

10

100

1000

10000

t (days) Fig. 9 Compression set (CS) of NR2 (Table 3) expressed as a percentage against duration of ageing (t) in hot air at stated temperatures (θ ). [CS of unaged reference testpiece was 0%.]


17

Fig. 10 Relaxation in compression for NR2 (Table 3). Force expressed as a percentage of the initial value (Fn) against duration (t) of ageing in hot air at 100°C.

In tension set, the unrecovered deformation of a strip of rubber is measured. Tension set is less often used but gives similar results to compression set – although comparison of Figures 9 and 11 suggests somewhat longer times to reach a given tension set than to reach the corresponding compression set. Again this illustrates that the aging results are dependent on the testing method chosen. The compression method may be a more severe test than tension set because of differences in the testpiece geometries and deformations during the test. Also, it needs to be emphasised once more that choice of an appropriate criterion for service life will depend a lot on the particular application.

100

80 q (°C) 55

60 TSet

70 40

85

20 0 0.1

1

10

100

1000

10000

t (days) Fig. 11 Tension set (TSet) expressed as a percentage for NR2 (Table 3) against duration (t) of ageing in hot air at stated temperatures. (TSet of unaged reference testpiece was 0%.)

18


Tensile strength Elongation at break

100

Compression set

t0.5 (days)

Tension set

10

Relaxation in compression

1 0.1 3.30 20

3.10 50

2.90

2.70 100

2.50

2.30 150

2.10 200

1.90 1000/T (K–1) q (°C) 250

Fig. 12 Arrhenius plots for NR2 (Table 3) aged in air. Time to reduction of stated property by 50% or to 50% set (t0.5) against reciprocal temperature.

Arrhenius diagrams are a useful tool in evaluating the service life of materials, they can be drawn for all properties where there are property/time/temperature data. An example of this is shown in Figure 12, using data as in Figures 5- e.t. seq. (Curves were fitted by eye to the data points in all cases.) A number of remarks can be made on Figure 12. (a) As stated previously, quite different life predictions can be obtained from different test methods (for a given failure criterion expressed as % change in the property). And as noted earlier, the failure criterion can be higher for compression set and tension set than for other methods. (b) Nevertheless, for any given test method and failure criterion the data do lead to straight line Arrhenius plots for predicted lives ranging from ~5 hours to ~3 years. This straight line behaviour indicates the utility of the method and indicates that the Arrhenius equation (with a single dominant activation energy) applies over rather wide ranges of time and temperature. (c) However, for different test methods different slopes – implying different activation energies – are observed in the Arrhenius plot (Figure 12). Compression set and stress relaxation data give very similar slopes (the highest); tensile strength and tensile set give similar and (lower) slopes; elongation to break gives a lower slope again. The differences in slope suggest testpiece-dependent effects and/or different ageing mechanisms for the different methods. In particular, when the different test methods are used to give Arrhenius plots, (50%) compression set usually predicts lifespans lower than those given by other methods with a 50% change in measured property used as the failure criterion. The area exposed to oxygen is low during the compression set test so it might be expected that it would give good ageing results, however compression set is closely related to relaxation behaviour – which is not highlighted in most other tests. Moreover, as stated earlier the different geometry and conditions may lead to the compression set test being more severe than tension set.


19

10000 1000

Tensile strength Elongation at break

100

Compression set

t0.5 (days)

Tension set

10

Relaxation in compression

1 0.1 3.30 20

3.10 50

2.90

2.70 100

2.50

2.30 150

2.10 200

1.90 1000/T (K–1) q (°C) 250

Fig. 13 Arrhenius plots for EPDM24 (Table 3) aged in air. Time to reduction of stated property by 50% or to 50% set (t0.5) against reciprocal temperature.

Remarks (a)-(c) are generally valid but other materials may be based on polymers of different chemical structure and other aspects of composition may also differ, thus the activation energies as well as the rates of chemical reaction are likely to differ – as are the influences of oxygen and other environment conditions. In the Arrhenius plots, both the slope and position of the line will consequently be affected. In Figure 13 Arrhenius plots for an EPDM cured with peroxide (EPDM24, Table 3) are shown. EPDM materials are less affected, than are NR materials, by thermo-oxidative degradation – especially when a peroxide cure (vulcanisation) system is used as in this case. For the EPDM24 the Arrhenius plots for 50% reduction in elongation at break, compression set and for 50% tension set all have a similar slope and intercept whereas the plots for tensile strength and relaxation in compression coincide at another slope and intercept. Other EPDM materials with different compositions and vulcanisation systems (viz sulphur) can exhibit different behaviour – for details see Andersson (1999). Note however that this EPDM material (EPDM 24, Table 3) can be expected to perform satisfactorily at 100°C for a period of about 6 months to two years depending on the application and criterion used to assess ageing performance. OTHER ENVIRONMENTS

Exposure to water or oil may affect the ageing of the material. A few examples of this are shown in Figures 14 to 17; the material (NR2, Table 3) is aged in water just below boiling point. For NR2 (Table 3) aged in water, both tensile strength and elongation at break decrease in a similar way to that for ageing in air – although at a rather lower rate. However for in-water-ageing the hardness changes in a completely different way from that found for in-air ageing: in water the hardness decreases rather than increases (Figure 16). A principal reason for the marked difference between the changes in hardness in air and in water is revealed in Figure 17; here it is seen that in water at 95°C the material swells to a considerable degree – which is not observed for in-air ageing. (For a discussion of diffusion of water in rubbery materials see Muniandy et al, 1988.)

20

Elastomers and Components: Service Life Prediction – Progress and Challenges 120

80 EBN 40

0 0.1

1

10

100

1000

10000

t (days) Fig. 14 Elongation at break (normalised by the value for the unaged material and expressed as a percentage, EBN) for NR2 (Table 3) against duration (t) of ageing in tap water at 95°C.

As pointed out earlier, ageing is often primarily due to thermo-oxidative reactions. When testing in media other than air at normal pressure, the oxygen content will strongly influence the results. In the tests reported here, different methods were employed to replace water lost during the test and thus oxygen content of the surrounding media. Thus no Arrhenius diagrams are drawn for ageing in water. At higher temperatures water must be pressurised during the tests and it is complicated to keep oxygen content constant. At higher pressures other effects may also influence the results; some polymers are susceptible to hydrolysis while others are affected in other ways. 120

80 TSN 40

0 0.1

1

10

100

1000

10000

t (days) Fig. 15 Tensile strength (normalised by the value for the unaged material and expressed as a percentage, TSN) for NR2 (Table 3) against duration (t) of ageing in tap water at 95°C.


21

120

80 HN 40

0 0.1

1

10

100

1000

10000

t (days) Fig. 16 Hardness (normalised by the value for the unaged material and expressed as a percentage HN) for NR2 (Table 3) against duration of ageing (t) in tap water at 95°C.

The data presented in Figure 18 suggest that at higher temperatures and pressures this EPDM material (EPDM24, Table 3) becomes plasticised by the water. It seems that the effects of plasticisation outweigh those of normal ageing and mask them – which could lead to erroneous conclusions. Once again this shows that data from more than one type of test are normally needed to evaluate ageing and make lifetime predictions. More details of tests on this and other materials are to be found in Andersson (1999).

100 80 60 40 VN 20 0 – 20 – 40 0.1

1

10

100

1000

10000

t (days) Fig. 17 Percentage increase in volume (VN) of hardness testpiece of NR 2 (Table 3) against duration of ageing (t) in tap water at 95°C.

22


Water (95°C) Water (125°C)

140 120 EBN 100 80 60 40 20 0 0.1

1

10

100

1000

10000

t (days) Fig 18 Elongation at break (normalised by the value for the unaged material and expressed as a percentage , EBN) for EPDM24 (Table 3) against duration (t) of ageing in tap water at 95°C and 125°C.

160

120 Oil 1 (70°C) Oil 1 oxidised (70°C) EBN 80

Oil 3 (70°C) Water (95°C) Water (125°C)

40

0 0.1

1

10

100

1000

10000

t (days) Fig. 19 Elongation at break (normalised by the value for the unaged material and expressed as a percentage, EBN) for FPM37 (Table 3) against duration of ageing (t) in tap water at 95°C and 125°C and in three oils at 70°C.

OILS

Many rubbery materials are affected by oil that is absorbed and causes the material to swell. Such swelling affects the mechanical properties: the rubber becomes softer, the tensile elongation may increase and tensile strength decrease – but the oil does not normally cause the material to age in the thermo-oxidative sense. Rubbery materials that are to be used in direct contact with mineral oil are generally made of polymers which have a high resistance to many other chemicals as well; often coupled with this is a high resistance to thermal and thermo-oxidative degradation.


23

100000 Tensile strength Elongation at break

10000 1000 t0.5 (days)

100 10 1 0.1 3.30 20

3.10 50

2.90

2.70

2.50

2.30

100

2.10 200

1.90

1.70 300

1.50 1000/T (K–1) q (°C) 400

Fig. 20 Arrhenius plots for FPM37 (Table 3) aged in air. Time to reduction of stated property by 50% (t0.5) against reciprocal temperature.

To enable service life prediction in a range of applications it is of equal importance to age the materials in oil as in air or water. In Figure 19 one example of prolonged exposure of a fluorocarbon rubber (FPM37, Table 3) to different oils and water is shown. Prolonged exposure, of up to 5 years, to oils at 70°C has a limited effect on this material (FPM37). After one to two years some reduction of elongation at break does occur. After 5 years oil no 3 affects the rubber more than the other two oils but the material still retains approximately 70 % of the extensibility it had in the unaged state. The water at 95°C does have a minor effect on the material and, despite the material’s high resistance to oils, at high temperatures (125°C) and pressure the water does have a very significant adverse effect on the material. Water at 95°C was found to have a significant effect on behaviour for 3 other flurocarbon rubbers tested (Andersson, 1999) so some caution must be exercised in applications where fluorocarbon rubber materials are exposed to water or steam at high temperatures. Once again it is important to carefully examine all possible environmental conditions when selecting a material for a demanding application. The high chemical stability of fluorocarbon rubber materials in air is manifested in their ageing performance; in Figure 20 (for FPM37, Table 3) the timescale of the graph is extended to 100 000 hours (compared with 10 000 hours in Figures 12 and 13) to reflect this. If the service life criterion is a 50 % reduction in elongation at break, the material can withstand 200°C in air for about one year. When tested at 150°C no significant change in the tested property was observed during the 5 year test. Using the Arrhenius plot in Figure 20, this fluorocarbon material is expected to last for 20 years in air at 150°C. Due to the costs involved, life estimation for such long lifespans are only practicable using accelerated tests.

6 CONCLUSIONS The main purpose of the programme described has been to obtain and study a set of data on as wide and representative a range of elastomeric materials as possible, covering a large but

24


consistent range of testing methods and temperatures. The accelerated ageing times are much longer than in other comparable studies. The number of properties that are tested is also large and many conclusions can be drawn from the resulting body of data. The main focus of the programme has been on thermo-oxidative ageing in the unstrained state. However, other influences on the long-term performance of elastomeric materials – such as those of water and oils at elevated temperatures – have also been considered and have been found to sometimes have a very marked effect. Some salient points are listed below. (a) For a wide set of materials and conditions, Arrhenius plots of logarithmic time to “failure” (according to a given criterion) against T-1 (where T is absolute temperature) have been found to be essentially linear. This has again underlined the wide validity and utility of the Arrhenius method. (b) Ageing causes some measures of material properties to decrease more quickly than others – some properties may even increase. Hardness for ageing in air is one property which increases with ageing. Thus it is very important to select the most critical property for lifespan prediction in a given application; it is equally important to choose a test method that adequately tests that property. (c) Different properties give different slopes for the Arrhenius plots, indicating the influence of different test methods which highlight different chemical processes.

7 FINAL REMARKS The main focus of the programme reported here and in Andersson (1999) has been on accelerated ageing and on the interpretation of test results using the Arrhenius plots. Other methods to predict ageing can also be used. A particularly thorough review of ageing tests, methods of evaluation and results have been issued by RAPRA (Brown et al, 2000). The technique of using accelerated tests, and interpretation of results with regard to known physical and chemical phenomena are reviewed for most methods applicable to rubber. Brown et al (2000) also list and comment on 287 abstracts relevant to ageing. The report underlines the validity of the Arrhenius equation to predict ageing but also highlights the caution that has to be exercised when using any accelerated tests. Brown & Butler (2000) have studied non-accelerated natural ageing over an unusually long period: 40 years. This extensive study, comprising 19 elastomeric materials (from 10 polymer types) was conducted with the testpieces in an unstressed state. 9 properties were measured at increasing times. The climate was an important variable: 3 different natural climates (moderate, hot dry and hot wet) were used. The main results are that natural ageing for elastomeric materials at ambient temperature is generally slow. Changes in properties due to natural ageing do occur and vary according to material and property evaluated, but in all cases the changes were within normal permissible limits. The authors conclude that although the materials had aged to a certain degree, all the materials in the study were still useable in a suitable application after 40 years storage. Thus the chemical processes occurring in the material at ambient temperature but without influence of external factors such as light, mechanical load and environmental influences (excluding moisture and normal temperature variation) do not cause sufficient changes in the material to make them unusable in a suitable application. As the temperature varied during the tests and no elevated temperatures were used, no


25

Arrhenius plots were produced. The results are extremely valuable to all applications subjected to mainly natural ageing. However, whenever higher temperatures or other environments other than those considered are encountered there is need of further data such as presented here and by Andersson (1999).

REFERENCES Andersson C (ed) (1999) Lifespan of Rubber Materials and Thermoplastic Elastomers in Air, Water and Oil IFP – The Swedish Institute for Fibre and Polymer Research, Mölndal, Sweden. ASTM D 3045 – 92 (1997): Standard Practice for Heat Aging of Plastics without Load, American Society for Testing of Materials. Barnard D & Lewis PM (1988) “Oxidative ageing” in Natural Rubber Science and Technology, AD Roberts (ed), Oxford University Press, 621-678. Brown RP, Forrest MJ, & Soulanget G (2000) “Long-term and accelerated ageing tests on rubbers” Rapra Review Reports 10, (2), RAPRA Technology Ltd. Brown RP & Butler (2000) Natural Ageing of Rubber – Changes in Physical Properties over 40 Years RAPRA Technology Ltd. DIN 53446 (1962) – as ISO 2578. ISO 37 (1994): Rubber, vulcanized or thermoplastic – Determination of tensile stress-strain properties. ISO 48 (1994): Rubber, vulcanized or thermoplastic – Determination of hardness (hardness between 10 IRHD and 100 IRHD). ISO 188 (1982): Rubber, vulcanized – Accelerated ageing and heat resistance tests. IEC216 – Publication 216, Guide for the Preparation of Test Procedures for Evaluationg the Thermal Endurance of Electrical Insulating Materials. ISO 815 (1991): Rubber, vulcanized or thermoplastic – Determination of compression set at ambient elevated or low temperatures. ISO 1817 (1985): Rubber, vulcanized – Determination of the effect of liquids. ISO 2285 (1995): Rubber, vulcanized or thermoplastic – Determination of tension set at normal and high temperatures. ISO 2578 (1993): Plastics – Determination of time-temperature limits after prolonged exposure to heat. ISO 3384 (1991): Rubber, vulcanized or thermoplastic – Determination of stress relaxation in compression at ambient and elevated temperatures. ISO 6914 (1985): Rubber, vulcanized or thermoplastic – Determination of ageing characteristics by measurement of stress at a given elongation. ISO 11346 (1997): Rubber, vulcanized or thermoplastic – Estimation of life-time and maximum temperature of use from an Arrhenius plot. Muniandy K, Southern E & Thomas AG (1988) “Diffusion of liquids and solids in rubber” Chapter 17 in Natural Rubber Science and Technology, AD Roberts (ed), Oxford University Press, Oxford, pp 820-852. UL-746B (1979): Polymeric Materials – Long term property evaluations, Underwriters Laboratories.

CHAPTER 2

Effect of Heat Ageing on Crosslinking, Scission and Mechanical Properties AR Azura School of Materials and Mineral Resources Engineering, University of Science, Penang, Malaysia AG Thomas Department of Materials, Queen Mary University of London, UK

SYNOPSIS There is a growing call to design engineering elastomeric components to meet demanding applications for a long guaranteed service life. Moreover, service temperatures are tending to rise, creating a more severe challenge for the materials. For example, current performance specifications for engine mounts often require the component to survive a large number of cycles at its maximum loading condition after it has been subjected to accelerated ageing tests. A research programme aimed at investigating possible mechanisms responsible for the change in the strength properties of rubbery materials when aged at elevated temperature has begun. The mechanisms explored are: increases in crosslink density, scission of the molecular chains, changes in the crosslink chemistry and hampering of the straincrystallisation process. The chapter presents experimental data for two natural rubber materials, one with an efficient (EV) and one with a conventional sulphur cure system,when aged at 100°C for periods of up to 112 hours. Tobolsky’s two-network theory has been used to estimate the degree of main chain and cross-link scission and formation of new cross-links from the stress-strain behaviour of the aged and unaged compounds in tension. Also presented are the strength properties of materials measured using standard trouser tear tests, cyclic fatigue and crack growth tests.

1 INTRODUCTION Ageing is the deterioration of desirable properties during storage or service. This is a phenomenon common to a wide variety of natural and synthetic elastomers including natural rubber (Cain & Cunneen, 1962). Various changes can occur in an elastomer component as a result of the conditions under which it is used or stored (Lindley, 1974; Davies, 1988). 27

28


Industrially important aspects of ageing include changes in physical properties such as the tensile strength, the hardness or the modulus of elasticity. If the conditions are too severe, the rubber may rapidly become unserviceable. The ageing process of natural rubber is complex but it is known that oxidation is a significant degradation process. The rate of degradation is significantly accelerated at higher temperatures. A discussion of the influence of ageing on the ability of natural rubber to strain-crystallise is given by Azura et al (2003). They find that reduced ability to strain crystallise is a plausible explanation for part of the reduction of strength on ageing of this material.

2 TWO-NETWORK THEORY During ageing, chemical changes occur within the network, which can result in scission of chains or of crosslinks and in formation of new crosslinks. The work reported here is concerned with methods of separately quantifying the three processes. It is believed that the processes are not affected by the imposition of a moderate static strain, such as 100%, during ageing. However, new crosslinks will form in the strained state, giving a second network. The Tobolsky two-network model (Tobolsky, 1960) combined with the basic statistical theory of rubber elasticity (Treloar, 1975) can be used to interpret the properties of samples aged in unstrained and strained configurations and to separately quantify the different ageing mechanisms. Previous work by Thomas (1974) and Pond & Thomas (1979) has shown that high stresses even at room temperature can produce the rupture of chemical bonds or crosslinks in rubber vulcanisates. Some new crosslinks were also formed. They estimated the numbers of scissions and reformations from measurement of permanent set and equilibrium swelling, using the Tobolsky two-network model. In order to study the effect of ageing on crosslink breakage and recombination, the same approach has been used here. In addition, equivalent values are estimated below from the stress measurements. 2.1 STRESS MEASUREMENTS FOR TWO-NETWORK THEORY

The two-network model (Tobolsky, 1960) can be used to establish the number of crosslinks formed during the ageing process, from a comparison of the stress-strain behaviour of testpieces aged with and without pre-strain. The stress versus extension relationship for a sample unaged, and aged with and without 100% pre-strain gives useful information about the number of original active chains that contribute to a particular stress at particular extension (in this case at 100% leading to the M100 engineering stress). The results were interpreted on the assumption that any crosslinks formed in the particular strained state do not contribute to the stress at that particular extension (Tobolsky, 1960). As ageing continues, the testpieces aged in the strained state become softer since stress at that strain (M100) is reduced by the scission of the main chains together with loss of original crosslinks. For a testpiece aged in the unstrained state this loss in stress at that particular strain would be offset by the formation of new crosslinks. The illustration in Figure 1 gives an indication of factors that might influence the stress. From Figure 1, the differences between stress for unaged and aged samples with different ageing conditions (with and without 100% pre-strain) were interpreted as follows.

Effects of Heat Ageing

29

Fig. 1 Stress (σ) as function of length (l) for calculation of chain and/ or crosslinks scission and crosslinks reformation based on stress values read off at 100% strain for conventionally cured NR-unaged and aged for 48 hours at 100°C. (d is the set. The initial length of testpiece is 100 mm).

(i) The reduction, ∆N, in the total number of active chains per unit volume (N) going from an unaged sample to a sample aged without pre-strain is affected by: scission of the main chains (Nsc), scission of the crosslinks (Nsx) and the formation of the additional crosslinks (N2). Thus (1) (Note that scission of one crosslink reduces the number of active chains by two.) The overall fractional contribution to the stress can be calculated from

(2) where A is the stress read off from an unaged sample and B is stress read off from a sample aged without strain. (ii) The reduction Ns in the original number N of active chains per unit volume, going from an unaged sample to a sample aged with 100% pre-strain is affected by: scission of the main chains (Nsc) and scission of the crosslinks (Nsx). Thus

30


(3) The overall fractional contribution to the stress can be calculated from

(4) where C is stress read off from a sample aged with 100% pre-strain and Ns is the total number of original active chains lost. (iii) The proportion of active chains per unit volume, N, that remained unbroken for a sample aged with 100% pre-strain can be calculated from

(5) (iv) N2 [q.v. (i) above] can be calculated from stress measurements made on a deformed testpiece aged unstrained (B) and one aged at 100% strain (C) as follows

(6) 2.2 PERMANENT SET AND EQUILIBRIUM SWELLING MEASUREMENTS FOR TWO-NETWORK THEORY

An alternative technique to stress measurements is to determine the permanent set and the equilibrium swelling measurement of rubber network in a non-volatile solvent. Suppose that there are initially N cross-links per unit volume in the testpiece. On stretching, N1 of the original N chains remain active with Ns crosslink and/or main chain scissions and N2 new active chains formed through addition of crosslinks in the strained state. The permanent set is given by the Tobolsky two-network theory (Pond et al, 1979; Thomas, 1974) as:

(7) where

is the set extension ratio.

In order to study the effect of ageing on cross-link breakage and recombination during ageing, the samples were aged at 100°C (without strain and at an extension ratio = 2). The samples were then swollen to equilibrium in n-decane. After drying, the permanent set of the sample aged under strain, λxs , was measured. (The swelling and drying process is


31

believed to bring time-dependent recovery to completion.) The results for equilibrium volume fractions of rubber in swollen states for unaged samples (νr), samples aged with 100% pre-strain (νs) and fractional permanent set (λxs-1 ) were calculated. Ratios of the crosslinks breaking and crosslinks reforming as a fraction of original active networks were then calculated. Applying the usual Flory-Huggins relation between modulus and equilibrium swelling to the original single network and to the post ageing dual-network (Pond & Thomas, 1979), leads to:

(8) where χ is the polymer-solvent interaction parameter for the particular rubber-solvent system (0.41 for n-decane).

3 TEARING ENERGY CONCEPT The failure of most materials including rubbers appears to be due to the growth of cracks from inhomogeneities or flaws, which are initially presents and act as stress raisers (q.v. Busfield & Ng, 2005; Muhr, 2005). Thus the fundamental failure mechanism is that of crack propagation. It was found that when crack growth behaviour is expressed in terms of the elastic energy available for growth, tearing energy (T), the results are independent of the form of the test piece used (Lake & Thomas, 1988). Thus the relationship between the rate of crack growth and tearing energy represents a characteristic property of a rubbery material, which can be applied to predict the life for any type of deformation. The presence of a crack in a sample of material held at constant deformation reduces the strain energy stored in the sample by an amount which depends on the length of the crack. The tearing energy (T) [sometimes called the strain energy release rate] is formally defined as the decrease in the total strain energy (U) produced by unit increase in the area (A) of one surface of the crack (Rivlin & Thomas, 1953):

(9) where the subscript denotes that the deformation remains constant so that external forces do no work. The magnitude of the tearing energy can be calculated from readily measurable parameters for several simple test pieces. The tearing energy for the trouser test piece is given by:

(10)

32


where F is the tearing force acting on each leg of the specimen with uniform thickness t. In the above expression, the relationship between F and T is independent of the length of the initial cut. Alternatively, for the tensile strip which corresponds to the central parallel-sided part of dumbbell test pieces, the tearing energy is given by: (11) where W is the strain energy per unit volume obtained from area under a stress-strain curve or area under force-deflection curve divided by volume, c is the length of the cut in the unstrained state and k varies slightly with strain being given approximately by where λ is extension ratio (Lindley, 1972; Yeoh, 2005). The tensile strips are most suitable to investigate the characteristics of cut growth because they are easy to prepare and set up. The cut length can be readily measured and a wide range of tearing energy can be covered including similar tearing energies to those prevailing in many components under service conditions.

4 MATERIALS AND EXPERIMENTAL DETAILS Two unfilled natural rubber (NR) vulcanisates with two different curing systems (conventional and efficient sulphur) were used. Varying the ratio of accelerator (CBS) to sulphur (S) produces different types of crosslink chemistry. This in turn affects the accelerated ageing behaviour. 4.1 TWO-NETWORK THEORY

For the two-network theory studies, two sets of thin strips (0.5mm x 5mm x 100 mm) were aged with and without 100% pre-strain for different periods in an air-circulating oven at 100°C. The stress-strain measurements in tension were carried out using an Instron 4301 screw driven test machine with a cross-head speed of 100 mm/min. The test pieces were extended up to 300%. For swelling measurements, portions of test pieces from samples aged with and without 100% pre-strain were then swollen to equilibrium in n-decane. Ratios of the crosslinks breaking and cross-links reforming were then calculated as a fraction of original active networks as explained in Section 2.

Table 1 Formulations for efficient and conventional sulphur cured vulcanisates.(CBS is Ncyclohexylbenzothiazole-2-sulphenamide.)

Compounding Ingredients CBS / sulphur Natural rubber SMR CV 60 Zinc oxide Stearic acid Sulphur CBS Curing time at 150°C (min)

Formulation parts per hundred of rubber (pphr) Efficient sulphur system Conventional sulphur system 10 100 5 2 0.5 5 36

0.3 100 5 2 2.0 0.6 22


33

4.2 CUT GROWTH MEASUREMENTS

Tensile strips approximately 120mm x 25mm and 0.5 mm thick, were cut from vulcanised sheets both for unaged and aged samples. After stress-strain measurements of the strips have been obtained, the testpiece is then taken up to the required maximum extension and a cut about 0.5 mm long is made in the centre of one edge with a razor blade. Samples were then cycled on the in-house fatigue test machinesTARRC, Hertford. During the test, the cut (or crack) length c is measured with a travelling microscope fitted with an eyepiece scale, the strip being slightly strained to facilitate observation. Readings are taken at intervals of cycles ∆n corresponding to a 10-30% increase in cut length. The rate of growth (dc/dn) is determined from the increment in cut length divided by the number of cycles between two readings. This rate is referred to the tearing energy calculated from the average of the cut lengths and the strain energy density at the maximum strain of the cycle. 4.3 CATASTROPHIC TEARING ENERGY

Catastrophic tearing energy was determined using trouser test pieces 100 mm x 50 mm each with a cut to a depth 40 ± 5 mm in the direction of length. It is important that the last 1 mm of the cut is made by a razor blade. The test was carried out using an Instron 4301 screw driven test machine at rate of separation of 100 ± 10 mm/min. A steadily increasing traction force was applied until the test piece broke. The force throughout the tearing process was recorded using a chart plotter.

5 RESULTS AND DISCUSSION 5.1 STRESS AND PERMANENT SET AND SWELLING MEASUREMENTS FOR TWO NETWORK THEORY

Results in Tables 2 and 3 were calculated using stress-strain and swelling measurements. All the calculations for the net reduction in the number of original active chains in network are relative to the number of original active chains in the unaged sample. The net fractional change in the number of active chains was determined from the stress at 100% strain for the sample aged without strain and the fraction of original active chains that remained unbroken was determined from stress at 100% strain for the sample aged with 100% pre-strain (q.v. 2.1). The presence of permanent set suggests that some new crosslinks are forming. The reduction in stress at 100% for test pieces aged at 100% pre-strain is related to the number of original active chains that have been lost during ageing. The results show that for the conventional cure system the degree of main chain breakage, crosslinks reforming and the percentage of permanent set after ageing under 100% pre-strain are all greater than for the efficient cure systems. These results are not too surprising since conventional cure systems produce polysulphidic crosslinks, which are thermally unstable. The effect of ageing on crosslinks breaking and reforming calculated from permanent set and swelling measurements agrees quite well with that calculated from stress-strain results. As ageing continues the number of crosslinks breaking and reforming increases. For efficiently cured NR, the increase in new crosslinks is small compared to the crosslinks breaking throughout ageing. Conventionally cured NR shows a gradual decrease, with

34


Table 2 Crosslink breakage and reformation during ageing at 100°C for EV NR.

Ageing time

Methods

7 hours

Stress-strain Swelling Stress-strain Swelling Stress-strain Swelling

24 hours 48 hours

0.70 0.75 0.55 0.53 0.52 0.42

0.30 0.25 0.45 0.47 0.48 0.58

0.01 0.04 0.19 0.11 0.28 0.26

ageing time, in the fraction of original cross links remaining. These results were in agreement with results from stress-strain measurements, with most of the original cross links being destroyed for longer periods of ageing. The large increase in the fraction of new crosslinks was expected from the large amount of permanent set observed. To avoid inconsistencies elsewhere in the results, the effect of ageing on the number of crosslinks breaking and reforming were compared for the samples aged for 48 hours at 100°C. Results were calculated from swelling of samples aged without strain and aged at 100% strain. Conventionally cured NR shows about 80% crosslinks breaking with about 95% reforming, whereas in efficiently cured NR only 28% new crosslinks form with about 56% of the original ones lost. Results obtained from the stress-strain results for same duration of ageing agreed quite well with the swelling evaluation for the number of lost crosslinks but gave slightly lower values for the number of new crosslinks. After ageing for 48 hours at 100°C only about 22% of the original active chains per unit volume remained for conventionally cured NR and about 44% for efficiently cured (EV) NR. This result was in agreement with the fact that the crosslinks in conventional cured NR are thermally unstable and readily decompose from polysulphidic to di- and monosulphidic crosslinks. However, the interpretation in terms of the two-network theory of the stresses at 100% strain and the swelling results cannot distinguish between the effects of scission of crosslinks and scission of chains.

Table 3 Crosslink breakage and reformation during ageing at 100°C for conventionally cured NR.

Ageing time

Methods

7 hours

Stress-strain Swelling Stress-strain Swelling Stress-strain Swelling

24 hours 48 hours

0.48 0.66 0.12 0.33 0.12 0.19

0.52 0.34 0.88 0.67 0.88 0.81

0.26 0.28 0.63 0.56 0.72 0.84


35

dc/dn (cm/Mcycle)

100 Unaged Aged 3 days @ 100 C Aged 6 days @ 100 C Aged 3 days anaerobic @ 100 C 10

1

0.1 0.01

0.1 T (kJ/m 2)

1

Fig. 2 Crack growth rate (dc/dn) against tearing energy (T) for efficiently cured NR for different ageing times and conditions.

5.2 CUT GROWTH MEASUREMENTS

The main objective of the work undertaken here was to investigate the strength properties of the material after accelerated ageing. Tensile strips with edge cracks were used for cyclic crack growth measurements and trouser test pieces for catastrophic tearing energy measurements. The relationship between cut growth rate dc/dn and tearing energy T is referred to as the cut growth characteristic, since it represents the basic tearing property of the vulcanisate. Figures 2 and 3 show results for the crack growth rate over a range of tearing energies for various periods of ageing. Samples were aged at 100°C in an air-circulating oven for 3 and 6 days. For both the conventional vulcanisate and the EV material, the tearing energy required to achieve a given crack growth rate decreased with increasing ageing. Figure 2 shows that for a crack growth rate of 1 mm/Mcycle, the tearing energy for the EV material decreases by a factor of 1.6 for the testpiece aged for 3 days and a factor of 3.2 for the testpiece aged for 6 days when compared to the tearing energy for the unaged testpiece. Figure 3 shows the tearing energy, for the conventionally cured NR vulcanisate, at a crack growth rate of 10 mm/Mcycle decreased by a factor of 10 when the testpiece was aged for 6 days. At a rate of growth of 1 mm/Mcycle, tearing energies were higher, by a factor of about 3, for the unaged testpiece than for the testpiece aged for 3 days. It can be seen from Figures 2 and 3 that for testpieces aged for 6 days at 100°C conventionally cured NR exhibits higher crack growth rate than does the EV NR. The effects of ageing on the crack growth properties of the EV material were not as pronounced as that for the conventionally cured NR. This may be due to the fact that strain crystallisation is inhibited in the conventionally cured material as a result of ageing. The fact that chain modification occurs significantly in the conventionally cured material compared to the EV material agrees with this observation.

36


1000

Unaged Aged 3 days @ 100 C Aged 6 days @ 100 C Aged 3 days anaerobic @ 100 C

dc/dn (mm/Mcycle)

100

10

1

0.1 0.01

0.1 T (kJ/m2)

1

Fig. 3 Crack growth rate (dc/dn) against tearing energy (T) for conventionally cured NR for different ageing times and conditions.

Accelerated ageing and its effect on the cyclic crack growth has been investigated for aerobically and for anaerobically aged samples. The tearing energy for a crack growth rate of 1 mm/Mcycle is 2 times greater when a conventionally cured NR vulcanisate is aged in vacuo than when aged in the presence of oxygen. The data shows a similar effect for the EV NR. When aged anaerobically for 3 days the cyclic crack growth behaviour for the EV material remains essentially unchanged from that of the unaged material. However for the conventionally cured vulcanisate both aerobic and anaerobic ageing affected behaviour for the range of tearing energies investigated – although for aerobic ageing the effect was larger. The tear behaviour of rubbers is such that at a certain severity of deformation a tear or crack will suddenly increase in length by a readily visible amount – perhaps growing right across the testpiece. The magnitude of the load or deformation required to produce this catastrophic tearing will depend on the nature of the rubber and also on the type of testpiece used. However, if results are expressed in terms of tearing energy (T) then the onset of the catastrophic tearing can be defined by the critical value of T, Tc, which is independent of the form of testpiece used (Lake & Thomas,1988). Values for Tc measured using trouser test pieces are shown in Figure 4. The results shown are averages from 5 samples with standard deviations of about 0.54 kJ/m2 for conventionally cured system and 0.16 kJ/m2 for EV NR. The conventionally cured NR gives higher Tc for unaged samples but the value rapidly drops after ageing for 3 and 6 days. The tear strength of conventionally cured NR drops to 64.5% of the unaged value after ageing for 3 days at 100°C and to 89% after ageing for 6 days. For EV NR the drop in tear strength was about 33% (of the unaged value) after ageing for 3 days and 73% after ageing for 6 days. However, the initial strength of conventionally cured NR testpieces was 25% higher than that of EV NR testpieces.

37

Tc (kJ/m2)


Fig. 4 Effect of ageing on catastrophic tearing energy (Tc) (trouser testpieces).

6 CONCLUSIONS Main chain scission together with breakage and reforming of cross-links occurs during ageing. This leads to a deterioration in physical properties of natural rubber vulcanisates. We have observed that changing the cure system results in different accelerated ageing behaviour. Conventional systems show significant main chain scission plus new crosslink formation. While efficiently cured (EV) systems show principally crosslink breakage and main chain scission. Results from Tobolsky’s two-network theory show that for longer periods of ageing, almost all original active network chains were destroyed. The stress needed to stretch samples aged for longer periods arises from the formation of new crosslinks. The effects are more severe for conventionally cured NR with about only 20% of the original crosslinks remaining after ageing for 48 hours at 100°C, a factor of two lower than for EV NR. Results for the two-network theory applied to stress-strain data and swelling data give the same trends: an increase in the fraction of crosslinks reformed and broken during ageing. For 8 hours of ageing at 100°C conventionally cured NR gives about 10 times greater formation of new crosslinks with only 1.5 times more original crosslinks broken when compared with EV NR. The crack growth rate for a given tearing energy increased with the ageing time. The effect is more significant for conventionally cured NR than for the EV NR vulcanisate when aged at 100°C in air for 6 days. The tearing energy for a crack growth rate of 1 mm/Mcycle both for conventionally cured NR and for EV NR was 2 times greater after anaerobic ageing (at 100°C for 3 days) than after otherwise similar aerobic ageing. The decrease in catastrophic tearing energy after ageing for 6 days at 100°C was about 3 times greater for conventionally cured NR than for efficiently cured NR.

38

Elastomers and Components: Service Life Prediction – Progress and Challenges ACKNOWLEDGEMENTS

One of the authors, AR Azura, would like to thank Dr AH Muhr, Dr JJC Busfield and Mr HR Ahmadi for their help and guidance, TARRC for providing all the materials and equipment and the University of Science of Malaysia for the scholarship.

REFERENCES Azura AR, Göritz D, Muhr AH & Thomas AG (2003) “Effect of ageing on the ability of natural rubber to strain crystallise”, JJC Busfield and AH Muhr (eds), Balkema 79-84. Busfield JJC & Ng WH (2005) “Using FEA techniques to predict fatigue failure in elastomers” (This Volume). Cain ME & Cunneen JI (1962) “Fundamental approaches to ageing problems”, Revue Gen Caoutch, 39, 1940-1950. Davies B (1988) “The longest serving polymer”, Rubber Developments, 41, 102-109. Lake G J & Thomas AG (1988) “Strength properties of rubber”, chapter 15 in Natural Rubber Science and Technology, AD Roberts (ed), Oxford University Press, 731-772. Lindley PB (1972) “Energy for crack growth in model rubber components”, J Strain Analysis, 7, 132140. Lindley PB (1974) “Engineering design with Natural Rubber”, NR Rubber Bulletin, 15-20. Muhr AH (2005) “Fracture of rubber-steel laminated bearings”, (This Volume). Pond TJ & Thomas AG (1979) “Creep under repeated stressing”, International Rubber Conference, Venice, 3-6 October. Rivlin RS & Thomas AG (1953) “Rupture of rubber Part 1. Characteristic energy of tearing”, J Polymer Sci, 10, 291-318. Thomas AG (1974) “Factors influencing the strength of rubbers”, J Polymer Science: Polymer Symposia, 48, 145-157. Tobolsky AV (1960) “Stress relaxation in interchanging networks; viscoelasticity of interchanging networks; creep under constant load for interchanging networks” chapters 12-14 in Properties and Structures of Polymers, Wiley, New York. Treloar LRG (1975) “The physics of rubber elasticity”, 3rd edition, Claredon Press, Oxford. Yeoh OH (2005) “Strain energy release rates for some classical rubber testpieces by finite element analysis” (This Volume).

CHAPTER 3

Resistance of Bonds in Rubber Components to Corrosive Environments AH Muhr TARRC, Brickendonbury, Hertford, UK M Clotet and F di Persio Formerly TARRC, Brickendonbury, Hertford, UK Sanjay Solanki Rolls Royce, Bristol, UK

SYNOPSIS Rubber-to-steel bonded automotive components in temperate climates often suffer separation of the rubber from the steel, with corrosion evident on all exposed surfaces of the steel – including that originally bonded. The objective of this chapter is to clarify whether corrosion causes the bond to fail, or whether it merely attacks the metal exposed by the bond failure. This chapter shows that the phenomenon may be simulated in the laboratory, either by salt spray tests or simply by immersion in aerated salt solution. Since bond failure does not occur for rubber bonded to electrochemically passive substrates, such as nylon, and is greatly reduced in deionised water, it is concluded that it is electrochemical in origin. Possible mechanisms are discussed in the light of a review of similar phenomena observed with coatings for metal.

1 BACKGROUND The undersides of road vehicles in temperate countries are exposed to highly corrosive conditions, because of the use of salt to suppress ice formation on roads in the winter. Rubberto-steel bonded components in this environment often eventually suffer separation of the rubber from the steel, with corrosion evident on all exposed surfaces of the steel including that originally bonded. Although it appears that the corrosion could contribute to the bond failure, an alternative possibility is that the bond failure enables, rather than is caused by, the corrosion. Some rubber-to-metal bonded components are exposed to seawater, for example marine fenders and components for the offshore oil industry. One approach to increasing the 39

40


longevity of steel in such a highly corrosive environment is to use cathodic protection. In this technique, the electrochemical potential of the steel is reduced (i.e. it is “supplied” with electrons) in order to suppress the ionisation process: Fe → Fe2+ + 2ewhich is the first step in corrosion. Stevenson (1985a,b) studied the effects of salt water and of cathodic protection on natural rubber-to-steel (EN3B steel) bonds using as an adhesive the Chemlok 205-220 system. Cylindrical double shear testpieces were immersed in synthetic seawater either unstrained or with a static strain of 100% imposed. The steel was either unprotected, or subjected to cathodic protection by making an electrical connection to a zinc anode which was also immersed in the seawater electrolyte. The bonds were assessed by pulling them to failure in simple shear after selected periods of time. Over the time scale of the tests (1 year) no significant areas of bond failure were seen for the testpieces without cathodic protection for any of the temperatures used (3, 23 or 45°C), even though the exposed steel was corroded. However, progressive failure between primer and metal (PM) was seen for the cathodically protected testpieces; in severe cases this was evident even before shearing the testpieces to failure. Thus cathodic protection is effective at suppressing corrosion but is damaging to the bond. These observations would appear to indicate that corrosion has little relevance to bond failure, leaving the bond failure mechanism of automotive components a mystery and begging for further investigation. This chapter describes our efforts to this end; we have kept essentially to one filled natural rubber (NR) material, but vulcanisation-bonded it to a range of substrates (mild steel, stainless steel, aluminium and nylon 66) using several commercial solvent-based bonding agents, and exposed the testpieces to a range of potentially corrosive environments.

2 SALT-SPRAY TESTS Salt-spray testing (e.g. ASTM B117, 2002; BS 3900-F4 & F12, 1964 & 1997) was developed primarily for assessing the performance of paints and surface treatments for automotive applications. It has also become a standard test for rubber-to-metal bonded automotive components, and resistance to 1000h salt-spray is a typical requirement. Each automotive company tends to specify its own test environment and sequence – such as alternating periods of salt spray, drying, high and low temperature. Standard peel testpieces (ASTM D429, 1997; ISO 813, 1997) were prepared using the following sequence (note that trichloroethane has subsequently been withdrawn by the regulations): • • • •

degrease metal plates (63x25x2.5mm) in trichloroethane grit-blast with alumina (60/80 grade) degrease in trichloroethane apply either the Megum 3720 primer/100 topcoat system or the Chemosil 211 primer/220 topcoat system by handbrush • hot bond to NR (formulation in Table 1) by compression moulding for 25 minutes at 140°C Three different materials were used for the test plates – mild steel or stainless steel

Resistance of Bonds

41

Table 1 Formulation for rubber used in peel testpieces (ingredients by weight) SMR CV 60

SMR CV 60 ZnO Stearic acid N550 Struktol 410 UOP 88 Flectol H CBS Sulphur

100 5 2 28 2.8 4 2 1.5 1.5

(types 316 or 304). In the case of mild steel, some testpieces were subjected to a zinc phosphating pre-treatment (Gardobond 680, supplied by Chemetall Ltd) before applying the bonding agent by brush. A control set of testpieces was stored in the laboratory, while the “legs” of the other testpieces were tied back with string and they were hung in a saltspray cabinet for 4 weeks (673h) at 35°C. The test solution consisted of 50gL-1 NaCl (analytical reagent grade) in distilled water. After drying, the testpieces were pulled to failure in the usual 90° peel geometry (ISO 813, 1997). Results are given in Table 2. Most of the mild steel testpieces exposed to the salt-spray were found to exhibit encroachment of primer-metal (PM-type) failure from the edges of the testpiece, the exposed metal being light grey as if just grit-blasted, rather than rust-red as for the back of the test plate. Figure 1 shows a similar appearance for a testpiece that had been immersed in salt solution before peeling to failure. The interior of these testpieces, and all the others, exhibited predominantly rubber (Rtype) failure. The peel force was divided either by the testpiece width or by the width of R-type failure to give peel strength. The fact that the peel strength based on the R-type failure actually rose after the corrosive attack shows that a significant force is required to cause peeling in the PM-failure regions. Nevertheless, the presence of these regions does weaken the bond, and, being absent for stainless steel, the mechanism of the underbond attack leading to PM failure appears to be related to corrosion.

Fig. 1 Mild steel bond test plate after 5 weeks immersion in 5% NaCl solution

42


Table 2 Effect of 673h salt-spray on 90° peel test results

Substrate Bonding agent

Salt-spray

Depth of PM Peel strength over: penetration mm R, Nmm-1 all, Nmm-1

MS MS MS MS MS MS MS MS MS MS MS MS MS MS MS/P MS/P MS/P MS/P MS/P MS/P MS/P MS/P MS/P MS/P MS/P MS/P SS 316 SS 316 SS 316 SS 316 SS 316 SS 316 SS 304 SS 304 SS 304

n n n n n y y y y y y y y y n n n y y y n n n y y y n n n y y y y y y

5 7 8 7 3 2 6 6 6 7 6 5 5 7 patch patch patch -

205/220 205/220 3270/100 3270/100 3270/100 205/220 205/220 205/220 3270/100 3270/100 3270/100 220 220 220 205/220 205/220 205/220 205/220 205/220 205/220 3270/100 3270/100 3270/100 3270/100 3270/100 3270/100 205/220 205/220 205/220 205/220 205/220 205/220 205/220 205/220 205/220

Footnotes to Table 2 MS SS 205/220 3270/100 PM R -

12.0 14.7 17.5 18.2 19.3 12.6 13.2 10.3 12.5 15.8 16.3 14.9 13.0 23.6 18.1 17.2 15.4 11.4 11.8 11.8 22.1 17.8 21.2 13.7 11.6 16.3 18.1 17.4 18.3 18.3 17.4 17.9 17.6 17.8 17.4

mild steel (P-prephosphate treatment using Gardobond 680) stainless steel (types 316 and 304) Chemlok solvent-based system; 220 is topcoat on its own Megum solvent-based system primer-metal bond failure failure in the rubber

23.3 29.9 31.7 29.7 20.7 19.8 28.7 27.2 25.3

26.0 22.7 19.8

24.6 24.2 16.3

43

d (mm)

Resistance of Bonds

Fig. 2 Depth (d) of penetration of PM failure for peel testpieces immersed in aerated 50gL-1 brine

The results in Table 2 show that prephosphating of mild steel was in this case not effective, except for one test plate which showed only small patches of PM failure. The lack of protection could be a consequence of excessive storage of the phosphated plates (several days), in comparison to the suppliers’ recommendation of no more than a few hours before the primer is applied (Zellner, 1997). There was also no significant effect of omitting the Chemlok 205 primer from mild steel testpieces, showing that it is not effective at suppressing the PM failure in the salt-spray test. However, substitution of stainless steel (either 316 or 304 grade) eliminates the PM failure mode, except for occasional isolated patches.

3 IMMERSION TESTS Experiments were undertaken to see if the phenomenon of underbond “corrosion” occurs in a similar way in aerated brine as in a salt-spray cabinet. Since in the salt-spray tests underbond corrosion encroaches from the side of the testpiece, it evidently occurs even for an unstressed bond, so there is little to be gained by tying the peel testpiece legs back. The immersion tests included test plates of nylon 66, aluminium and mild steel. The testpiece preparation method and rubber were virtually equivalent to those used for the salt spray tests. The brine was prepared by dissolving salt granules for water softening (supplied by British Salt, and being at least 99.9% NaCl with Na2SO4 as the major impurity) in tap water at a concentration of 50gL-1, and was aerated by a bubbling tube connected to a cylinder of compressed air. Each type of testpiece was immersed in a separate glass beaker, so that there was no possibility of interaction (e.g. between aluminium and mild steel plates). The tests ran for 5 weeks with one testpiece of each type being withdrawn for peel testing (90°) each week. For mild steel test plates, the results were very similar to the salt-spray tests, underbond corrosion (giving PM-type failure) proceeding at about 1mm/week (see Figures 1 and 2). In the case of nylon 66 and aluminium test plates, there was no encroachment of PM-type

44


Table 3 Effect of substrate and bonding agent on underbond corrosion during immersion in aerated 5% NaCl solution (90° peel)

Substrate

Bonding Agent

Stainless steel 304 Aluminium Mild steel Mild steel Mild steel Mild steel Mild steel

Ch 211/220 Ch 211/220 Cil 22 Cil 21T Cil 12/80 Ch 211/220 Megaum 3270/100

Depth of corrosion (mm) after 1-5 weeks 1 2 3 4 5 0 0 0 patch 0 0 0 0 1 2.5 3 3.5 5.5 1 1 3.5 all all 0.8 3 4 5 5.5 1 1.8 2.1 3.5 3.5 0.7 2.2 3 3.2 3.2

failure from the bond edge up to the maximum test duration (5 weeks). As in the salt-spray test, there was no significant effect of omitting Chemosil 211 primer – the depth of PM failure after five weeks immersion was the same as for the testpiece using the full 211/220 system. There was also no significant difference in behaviour, with or without exposure to brine, if the UOP88 antiozonant was replaced by 3pphr HPPD and the Flectol H antioxidant omitted. The fact that this type of failure is seen with mild steel but not with stainless steel, nylon or aluminium strongly suggests that the mechanism is related to corrosion, and not just attack of the bonding agent by salt water. Further immersion tests of peel testpieces were carried out in aerated salt solutions and also in hydrochloric acid, sodium hydroxide solution, and deionised water. The results for the depth of underbond corrosion in NaCl solution (Table 3) are in accord with those of the first series of brine immersion tests (e.g. Figures 1 and 2) but show also that the Cilbond bonding systems Cilbond 12/80, Cilbond 21 and Cilbond 22 behave in a similar way to the Megum and Chemosil systems. Painting the exposed mild steel plate with Chemosil 211 primer did not have any significant effect on the depth of PM failure although it greatly reduced corrosion of the exposed metal. Results for the depth of underbond corrosion for the range of solutions investigated are given in Table 4. Underbond corrosion seems to occur at a similar rate in all the chlorides, but much more rapidly in sulphuric acid. There was negligible underbond corrosion over the test timescale (5 weeks) in deionised water or NaOH solution. Zinc phosphate pre-treatment (Gardobond 680) was found to be effective

Table 4 Effect of electrolyte on underbond corrosion of Chemosil 211/220 bonds to mild steel, during immersion in aerated solutions (30° peel)

Solution 0.86M NaCl 0.86M CsCl 0.86M KCl 0.43M H2SO4 0.1M NaOH deionised water phosphated, 0.86M NaCl

Depth of corrosion (mm) after number of weeks 1 2 3 4 5 0.5 1 1.8 1.5 2.5 0.5 0.6 1 1.5 1 0.4 0.8 1.8 2 2 3 6 7 7.5 9 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0

Resistance of Bonds

45

in suppressing underbond corrosion, although the exposed surface developed as heavy a rust deposit as for unprotected plates The peel tests were carried out both immediately after drying the testpieces off at the end of the immersion period, and after storing them in normal laboratory conditions for one week. There was no recovery, the depth of PM failure being the same in both cases.

4 MECHANISM OF BOND FAILURE IN CORROSIVE ENVIRONMENTS 4.1 NATURE OF METAL-PRIMER INTERFACE

Metal surfaces become covered by an oxide film (even if very thin) almost instantaneously after exposure to air and it is also believed that water molecules exist on this film, and hence between it and any organic film such as the primer, in all circumstances of practical interest (Koehler, 1982). The suggestion is that, in particular circumstances, this water can increase in quantity and displace the primer from the metal. For some systems, drying may result in reduction of the quantity of water and the adhesion may recover; for example, this has been observed for a Chemlok 205/220 coating with no rubber covering (Thornton et al, 1986). 4.2 OSMOSIS

The driving force for the accumulation of the interfacial water may be osmotic or may be associated with electrochemical reactions (Leidheiser, 1986). Boerio & Hong (1989) found that during cure, chlorinated rubber in Chemlok 205 primer and 220 adhesive (equivalent to Chemosil 211 and 220 respectively) undergoes dehalogenation. The evolved chlorine reacts with ZnO in the primer to form ZnCl2 at the primer-steel interface, which they suggested may contribute to delamination through osmotic effects. The possibility that the PM failure observed in the present work could be solely a consequence of an osmotic driving force can be rejected, since the phenomenon does not occur for stainless steel, aluminium or nylon substrates, and moreover does not occur for mild steel in deionised water, when the osmotic driving force would be greater than in salt water. 4.3 ELECTROCHEMICAL NATURE OF CORROSION

When iron is immersed in aerated water, it reacts with the oxygen and water to form hydrated iron oxide. The reaction takes place all over the surface, but may be considered to consist of the following steps: Fe → Fe2+ + 2eO2 + 2H2O + 4e- → 4OH2+ 3Fe + O2 + H2O + 6OH- → FeO • Fe2O3 + 4H2O black “magnetite” 2FeO • Fe2 O3 + 3H2O + O2 → 3Fe2 O3 • H2O red “rust”

(1) (2) (3) (4)

Because the electrons can travel freely through the metal, reactions (1) and (3) can occur at separate locations on the metal surface. We may then refer to (1) as anodic and (2) as cathodic; a similar situation could also be envisaged if two dissimilar metals are connected electrically – the less noble metal will become an anode and dissolve in the electrolyte

46


M → M2+ + 2e-

O2 + 4H+ + 4e- → 2H2O – acid O2 + 2H2O + 4e- → 4OH – neutral 2H+ + 2e- → H2↑ – in the absence of other reduction reactions

Fig. 3 Schematic corrosion cell

(Figure 3). Equilibrium reactions such as (1) and (2) have electromotive forces (emfs) associated with them, dictating which combinations of reactions are thermodynamically possible. However, the rates of the reactions are dominated by other factors, so for the present purposes there is little merit in listing standard emf values. It may be noted in Figure 3 that ions have to migrate to maintain the charge balance, and the rate of corrosion would be expected to be sensitive to the conductivity of the solution. 4.4 CREVICE CORROSION

In a crevice where oxygen cannot readily diffuse, such as the interface between an absorbent gasket and a metal flange, its concentration will fall. Only reaction (1) can then proceed, in this location, with reaction (2) occurring on the exposed surface and reactions (3) and (4) where the regions meet. Chloride ions can diffuse rapidly and, if present in the water, will diffuse along with OH- ions into the crevice to maintain the charge balance. The effect of the OH- ions on the pH in the crevice is very small, but the combination of chloride and iron (II) ions can reduce the pH to about 3:

(5) The presence of the Cl- and H+ ions increases the rate of the anodic dissolution, making the process autocatalytic (Sheir, 1994; Jones, 1996). This sequence of events is considered to be the mechanism of “crevice corrosion”, and, in the context of organic coatings, also of “anodic undermining” (Leidheiser, 1986; Amirudin & Thierry, 1996).

Resistance of Bonds

47

One possible mechanism of underbond corrosion noted for rubber-to-mild steel bonds in the previous sections could be crevice corrosion or anodic undermining. This leaves some puzzles, however. (i)

Why is the phenomenon not observed with type 304 stainless steel (see Table 2) which is “active” rather than “passive” in de-aerated salt water (Jones, 1996)? (ii) Why does the “etching” of the steel propagate under the bond quite rapidly but the depth of erosion of the steel is imperceptible? (iii) Why is there no obvious deposit of Fe(OH)2 at the interface? 4.5 CATHODIC DISBONDMENT

Paints and other organic coatings for corrosion protection often suffer progressive disbondment in the region surrounding a damaged area of the coating (called a “holiday” if introduced artificially – see for example BS 3900-F11). This is usually ascribed to “cathodic delamination” (Leidheiser 1986); the “holiday” serves as the anode, and, by virtue of permeability of the coating to ions and oxygen, the metal under the coating serves as the “cathode”. Disbondment seems to be a consequence of the generation of alkalinity (see Figure 3) at the “cathodic” interface (Thornton et al, 1986; Boerio & Hong, 1989). The process can be spontaneous, but can also be driven by an applied (negative) potential. If the latter is sufficiently large, an additional mechanism – evolution of hydrogen (see Figure 3) – can contribute to delamination. The mechanism is thus the “opposite” of that outlined in the previous section. Stevenson (1985a, b) found that NR is a very effective corrosion control coating (even if no bonding agent is used) owing to its low water permeability and low electrical conductivity; CR and NBR are rather less effective. As mentioned in Section 2, he has reported that disbondment occurs for testpieces immersed in salt water only if a cathodic potential is applied to the steel. He suggested that rubber-to-steel bonds could be susceptible to the conditions of high alkalinity generated at the cathode. Boerio & Hong (1989) found that the phenolic resin in Chemlok 205 primer is degraded by exposure to OH- ions. There are a number of problems with the hypothesis that spontaneous underbond “corrosion” occurs by cathodic disbondment. (i) Why is underbond corrosion accelerated in acid solution? Leidheiser (1986) stated that “no cathodic delamination occurs in pure acid solutions”. (ii) Why does no underbond corrosion happen in alkali solution? (iii) The rubber covering to the steel is typically quite thick, and it is difficult to see how the O 2, H + or H 2O species could reach the cathodic site by permeation through it. Interestingly, Leidheiser (1986) states that the area delaminated is generally related to the time at constant temperature and constant potential, whereas Stevenson (1986a, b) suggested the penetration depth of cathodic disbondment is proportional to the square root of time. Our results (Figure 1 and Tables 3 & 4) are more consistent with proportionality with time, suggesting a chemical rather than a diffusion controlled mechanism.

48

Elastomers and Components: Service Life Prediction – Progress and Challenges 5 DISCUSSION AND CONCLUSIONS

The mechanisms of underbond attack in corrosive environments, characterised by encroachment of primer-metal failure from the exposed bond edge, are not fully understood. Also, the story presented here is further complicated when other reports are taken into account – for example, Boerio & Hong (1989) found that CR (polychloroprene: Neoprene) bonds to steel, using the Chemlok 205/220 system, delaminated in molar NaOH solution whereas in this work 0.1M NaOH had no effect on similar bonds. However, the results reported in this chapter do give clear evidence that the driving force is electrochemical, rather than solely osmotic, in origin. A surprising result is that the primers, advocated by the manufacturers for enhancing the “environmental” resistance of the bonds, have no effect. This may be a consequence of the relatively low cure temperature used (140°C), since it has been suggested (personal communication) that the function of the primer is to protect the steel from any hydrogen chloride generated by decomposition of the bonding agent (top coat) at higher curing temperatures. The results of our tests conflict with the earlier work of Stevenson (1985a,b) that suggested that there is no effect of salt water on similar NR-mild steel bonds unless cathodic protection is used. Warren et al (1990) found that for CR to steel bonds, a correlation exists between resistance to salt spray and resistance to disbondment under an applied cathodic potential. They confirmed that for most bonding agents a calcium-modified zinc phosphate pre-treatment improved the resistance to salt spray, but surprisingly it actually made the most resistant system (Chemlok AP134/205/220) more susceptible. They did not try prephosphating for the testpieces subjected to cathodic protection, but it is known that such passivity breaks down at high alkalinity so it is not likely to be beneficial. Stevenson & Thomson (1998) have found that the effect of temperature on bond failure in seawater immersion tests is complicated by a strong effect of the dissolved oxygen level on the rate of failure. These features need to be borne in mind in carrying out laboratory assessments of susceptibility. As a general rule it is advisable to avoid exposure of the bond edge to the environment, and ideally the substrate should be totally encapsulated with rubber. Where this is not possible, the choice of substrate material and bonding agent can have a major influence on bond durability. Resistant substrates, such as nylon 66 and stainless steel, can greatly improve resistance of bonds in corrosive environments. Caution should, however, always be exercised and unless experience already exists with the materials (rubber, bonding agent and substrate) in the particular service environment an experimental assessment should be made. This should involve testpieces with exposed bond edges in as representative an environment as possible, thus avoiding pitfalls such as assuming that temperature will accelerate processes of interest.

REFERENCES Amirudin A & Thierry D (1996) “Corrosion mechanisms of phosphated zinc layers on steel as substrates for automotive coatings” Progress in Coatings, 28, 59-76. ASTM B117 (2002) : Practice for operating salt spray (fog) apparatus, American Society for Testing and Materials. ASTM D429 (1997) : Rubber property-adhesion to rigid substrates, method B, American Society for Testing and Materials.

Resistance of Bonds

49

Boerio FJ & Hong SG (1989) “Degradation of rubber-to-metal bonds during simulated cathodic delamination”, J Adhesion, 30, 119-134. BS 903: Part A21, Section 21.1 (1997) (also ISO813-1997), Adhesion to rigid substrates – 90° peel method, British Standards. BS 3900, Group F, Durability tests on paint films, British Standards. F4 (1964) Resistance to continuous salt spray. F11 (1985) Determination of resistance to cathodic disbonding for land-based buried structures. F12 (1997) Determination of resistance to neutral salt spray. Jones DA (1996) Principles and Prevention of Corrosion, 2nd Edition, Prentice Hall, New Jersey. Koehler EL (1982) “Underfilm corrosion currents in the course of failure of protective organic coatings”, Organic Coatings (NACE), pp 87-96. Leidheiser H (1986) “Mechanisms of de-adhesion of organic coatings from metal surfaces”, Chapter 12 in Polymeric Materials for Corrosion Control: an Overview, RA Dickie & FL Floyd (eds), ACS Division of Polymeric Materials Science & Engineering, Washington, USA. Sheir LL (1994) Corrosion, Butterworth-Heinemann. Stevenson A (1985a) “On the durability of rubber/metal bonds in seawater”, Int J Adhesion & Adhesives, 5, 81-91. Stevenson A (1985b) “The effect of cathodic protection on rubber/metal bond durability in sea water”, Proc of Discussion on Offshore Engineering with Elastomers, Plastics and Rubber Institute, Aberdeen, UK, June. Stevenson A & Thomson B (1998) “Life prediction for rubber/metal bonds: the role of elevated temperature in accelerated testing”, Proc Rubber Bonding Conference, Rapra, Frankfurt, Germany. Thornton JS, Cartier PF & Thomas RW (1986) “Cathodic delamination of protective coatings: cause & control”, Chapter 15 in Polymeric Materials for Corrosion Control: an Overview, RA Dickie & FL Floyd (eds), ACS Division of Polymeric Materials Science & Engineering, Washington, USA. Warren PA, Mouwrey DH & Gervase NJ (1990) “Adhesives for bonding cathodically protected rubber-to-metal devices”, paper 31, ACS Rubber Division, Fall meeting, Washington, USA. Zellner A (1997) “Aqueous chemical pre-treatments for rubber-to-metal bonding”, Rubber Technology International ’97, 100-104.

CHAPTER 4

Assessment of Life Prediction Methods for Elastomeric Seals – A Review JR Daley Trelleborg Sealing Solutions, Ashchurch, Tewkesbury, Glos., UK

SYNOPSIS The prediction of the life of a sealing element within a system is required to allow planned maintenance to be carried out at the most efficient time. In the automotive industry there is a trend for seals to last for ever increasing amounts of time, with the latest goal being 15 years (150 000 miles). With greater life times required, methods have to be adopted to predict the life of the seal in application, and accelerate testing to allow this to be completed in an acceptable time period. In this chapter several common methods of prediction for static seals are reviewed and their applicability to the actual sealing application environment assessed.

1 INTRODUCTION Increasingly, the sealing industry is being faced with the question of component service life: how long will components last? This apparently simple question is one which is certainly difficult to answer and impossible to without putting a considered margin around the life prediction figure. Static seals, such as gaskets and O-ring seals, are used in all industries. Restricting ourselves to static seals eliminates the complications of dynamic interactions and factors such as wear, friction and tribological effects (Hertz, 1992), which all add to the degradation of the seal (and mating surface), and hence may affect seal life (Coveney & Menger, 1999, 2000; Menger, 2001). For static seals the primary considerations are the changes in the properties of the elastomer with time, and the effect of these changes have on the sealing ability of the seal. Any of the following, and combinations thereof, can lead to seal failure. • • • •

Relaxation and compression set of the seal Excessive hardening Chemical attack Explosive decompression (ED) 51

52 • •

Elastomers and Components: Service Life Prediction – Progress and Challenges Incompatible thermal expansion Extrusion damage

Service life of elastomer seals is limited by the interaction of the polymer with its environment (temperature, pressure and chemical), and is affected by changes in the characteristics of the elastomer over time, and the design of the seal. General discussions on material selection for seals are given elsewhere (see for example Eason & Barnes, 1994). Here I consider seal life, and the methods of predicting the life expectancy of static seals.

2 STRESS RELAXATION AND SET Compression set and compressive stress relaxation are normally the key issues when considering static seals. [Coveney & Rizk (2005) and Morgan et al (2005) consider other causes of failure.] The loss of the sealing force during the life of a seal under compression is well known (Bunting et al, 1992). There will in the seal’s life come a point when the retained sealing force is inadequate to overcome the leakage pressure of the fluid, and hence the life of the seal is at an end. The actual point at which this occurs is, however, open to debate, and is certainly a function of applied pressure – low pressure sealing is particularly susceptible to leakage, when the material has lost compliance to provide sealing, in comparison with higher pressure applications where the seal is often forced into providing a high enough contact stress to prevent leakage [pressure activated sealing (Coveney & Rizk, 2005)]. Stress relaxation (and set) can be considered to be as a result of “physical” (i.e. viscoelasticity-related) and chemical effects. Generally, physical relaxation proceeds approximately linearly (but perhaps more accurately logarithmically) with logarithmic time and is often overtaken by chemical relaxation which proceeds approximately linearly with linear time (Stevenson & Campion, 1992). In order to predict the failure point in the future, Arrhenius, and WLF (Williams-LandelFerry transform) methods may be used [Huy & Evrard, 2000 and Equation (1)]. Arrhenius plots are mainly used to predict chemical, e.g. oxidative ageing [Albihn, 2005 and Equation (2)] while the WLF transform is often employed to predict viscoelastic effects. In practical applications there is often a combination of both physical and chemical effects occurring in parallel, which can lead to difficulties. The stress relaxation curves for an elastomeric material, are shown in Figure 1. The three curves correspond to the three test temperatures (160°C, 180°C and 200°C), with the higher test temperature resulting in the highest relaxation rates. The data was collected using continuous compression stress relaxation (CSR) measurement as outlined by Spetz (2000). The results below are from tests carried out in air, in application seals are used in numerous fluids and, where exposure is seen, the compression tests must be carried out in the fluid concerned (Stevens, 2000) to ensure any related physico-chemical effects are taken into account. A (WLF based) shift of data is shown in Figure 2 – from 200°C, where the most data was collected, to the lower temperatures of 180°C and 160°C. [See Equation (1), below and Ferry, 1992.] In Figure 2 the measured data is shown in black, and the transposed data in grey. Increasing the test temperature accelerates the viscoelastic relaxation rate of the material. At the lower temperatures, more time is required than at higher temperatures for the material to reach the same state of stress relaxation. It may be seen that to reach a 50% loss in initial force

53

Fn

Assessment of Life Prediction Methods

Fig. 1 Compressive stress relaxation (CSR), plot of force (Fn) normalised to initial value against time (t) in hours of a fluorocarbon elastomer FKM [upper, middle and lower curves are for 160°C, 180°C and 200°C respectively.]

1 0.8

Fn

0.6 0.4 0.2 0 1

10

100 t (h)

1000

10000

Fig. 2 WLF transform applied to CSR data from FKM – q.v. Figure 1. Plot of force (Fn) normalised to initial value against WLF-shifted time (t in hours). [Upper, middle and lower curves are for 160°C, 180°C and 200°C respectively.]

requires 150 hours at 200°C, and 2000 hours at 160°C. Hence a significant reduction in laboratory test time is achievable, provided that the data may be accurately extrapolated. The data from the shorter term, higher temperature test is used by transposing it onto the lower temperature test results. The curves fit well, and the form of the curves are correct, and this method may be used for extrapolation. Both the WLF [Equation (1)], and the Arrhenius [Equation (2)] plots allow a prediction of long term material behaviour using measurements made over shorter timescales, such as

54


seen in Figure 1. The extrapolations are made on the assumption that the methods are valid and that there that there are no unaccounted for effects impinging on the relationship between the material property and time. Unfortunately, the methods of extrapolation suffer from two major sources of error. One of the sources of error relates to the paucity of data. Testing is time-consuming and in the case of the Arrhenius method only one data point is utilised per test – e.g. the point at which a given property falls to 50% of its initial value. Thus practical limits are imposed on precision. The second source of error concerns the extrapolation of the data points from short term (more accurate) to longer (increasingly less accurate) time frames (see also Albihn, 2005). Moreover, during long tests problems with fluctuating conditions, drift etc can be significant. One form of the WLF transform equation is (Ferry, 1992):

(1) where C1 and C2 are material constants, T is the temperature, and T0 is the reference temperature. The Arrhenius equation is: (2) where k is the rate (e.g. of a chemical reaction), A is a constant, Ea is the activation energy of the mechanism, R is the universal gas constant, T is the absolute temperature. If the failure process conforms to the Arrhenius equation it follows that a plot of log(life) against T -1 is a straight line (see Albihn, 2005). By means of Arrhenius plots, service lives are often extrapolated from the material’s property curve, for the temperature required. However (see above and Albihn, 2005) these extrapolations are not without risk. The data in Figure 1 has been transferred to such a plot in Figure 3. Despite the fact that the stress relaxation process for this material are believed to be primarily “physical” the Arrhenius plot is approximately straight, suggesting the utility of the method. [Mechanisms of stress relaxation are discussed by Fuller (1988), Chapman & Porter (1988), Barnard & Lewis (1988) and Azura & Thomas (2005).] The “failure” criterion is often conservatively set at 50% loss of original force. The graph indicates the expected time it would take, at a given temperature, for 50% of the original compressive force to be lost. In reality, significantly more than 50% of the original value must be lost for leakage to occur. These two methods (WLF transform and Arrhenius plot) give methodologies for the use of reduced time laboratory test data. An indication of the relaxation / set behaviour of the elastomer or seal is thereby obtained but these methods do not give a prediction of whether the seal will operate for a given period of time. Rather, a comparison of materials is given. With this data the choice of one material over another for a given target life may be made. In order to make satisfactory life predictions for the seal an understanding of modes of operation and failure is required. Finite element analysis (FEA) can greatly assist - especially in the case of complex geometries.

55

t (yrs)


Fig. 3 Arrhenius plot applied to CSR data from FKM – q.v. Figure 1. Time (t) to 50% of original force against reciprocal of absolute temperature (T). [Extrapolation to T-1 = 0.0027 K-1 corresponds to 97ºC.]

3 FINITE ELEMENT ANALYSIS In order to estimate the life of the seal non-linear finite element analysis methods (FEA or FEM) have been used. FEA allows the modelling of both simple and complex crosssections of seals, and hence is useful for assessing the change of stress within complex seal geometry and the effect on its sealing performance. For FEA performed on a seal, when the sealing force per unit area (contact pressure) becomes less than the system pressure this is generally taken to indicate the onset of leakage. It should be noted that in FE models the seal surface and the mating faces are assumed to be perfectly smooth – ignoring the possibility of “seepage” along a scratch on the metal housing, for example. Also the possibility of adhesion is generally ignored. In order to accurately model the life of a static seal, material data is key. Initial data may be precisely tested for, and included in the model (Daley & Mays, 1999), but the material properties change over the life of the seal. The seal may swell due to interaction with the contained fluid, the physical properties can change due to oxidation, and fluid effects, and the sealing force will drop due to stress relaxation. Although many have modelled specific elements of a seal in operation, no one has put a unified FEA model together to fully simulate the life of a seal. The various aspects, which have been modelled, in addition to hyperelastic behaviour, include: permeation (Ho, 2001; Ho & Nau, 1996); explosive decompression (Ho, 2000); fatigue (Busfield, 2001). Modelling of the aspects listed above has been done, with good reason, to assess the most likely failure mode for the application. However, without full interactive account being taken of the chemical and physical changes within the seal, uncertainty is introduced in the precision of the prediction. As discussed above, in the case of a static seal, compressive relaxation is generally taken as the probable cause of failure. Sealing geometries range from the simple – such as the O-ring seal, as shown in Figure 4, to more complicated designs and loadcases – such as the gasket shown in Figure 5. [For

56


Fig. 4 Plots for 2-D hyperelastic finite element analysis (FEA) of an O-ring seal in pre-relaxed state (left) and following stress relaxation (right). Cauchy 22 stresses are shown (MPa). The FE code used was MARC.

Fig. 5 Stress plot for 3-D hyperelastic finite element analysis (FEA) of a gasket. The FE code used was MARC.

a discussion of hyperelastic modelling and FEA see Gough et al, 1999; Cadge & Prior, 1999.] The stress pattern in Figure 4 is simpler, more uniform, and easier to interpret, than the multifacetted loading of the gasket in Figure 5 – nevertheless the advantages of FEA are clear.

4 OTHER FAILURE MODES Other failure modes, such as explosive decompression or extrusion damage of the seal, are features which should be anticipated in design (Morgan et al, 2004). It is however the case


57

that the seal environment predicted and the actual conditions seen are not necessarily the same, and hence such failures do occur. Chemical attack of seals is seen in more aggressive environments, such as occur in the chemical industry, and here a service life of months rather than years is usually accepted. In considering more expensive materials, such as perfluoroelastomers, the cost / life benefit in the application must be weighed up (Daley & Phillips, 2000). Although use of perfluoroelastomers is a fairly extreme example, the type of elastomer must fit the application – and relevant fluids and temperatures – to ensure that chemical degradation of the seal is not accelerated. Further failure modes include mismatch of thermal expansion, especially if the elastomer seal does not recover quickly enough under thermal loading. A simple case is cold start testing, where the components are cooled, usually to -40°C, and then the engine is started. If the housing around the seal expands at a faster rate than the seal can follow, then a leakage path will occur. Low temperature elasticity of elastomers is commonly measured through low temperature retraction (TR) tests (ISO 2921,1997). In addition to the above factors which can be designed against, there can be damage to seals through assembly, transport or storage, which reduces their life span.

5 CONCLUSIONS Methods do exist to assess the lifetime of elastomer materials and seal designs, through accelerated testing and analysis. However in order to utilise the laboratory results there must be consideration of the environment that the seal actually experiences. In use, a seal will be subjected to a range of operating conditions; this range must be applied to the theoretical methods of seal life prediction. Therefore a combination of laboratory material tests, application testing, mathematical modelling, and application knowledge and experience is required for life prediction. Even then, this is a best guess estimate, due to uncertainties in the final application environment. Therefore, in practice, any prediction work carried out can only consider samples which experience typical or representative conditions which will occur in the application environment.

REFERENCES Albihn P (2005) “The 5-year accelerated ageing project for thermoset and thermoplastic elastomeric materials: A service life prediction tool” (This volume). Azura AR & Thomas AG (2005) “Effect of heat ageing on the strength properties of elastomeric components” (This Volume). Barnard D & Lewis PM (1988) “Oxidative ageing”, Chapter 13 in Natural Rubber Science and Technology, AD Roberts (ed), Oxford University Press, 621-678. Bunting WM, Russell WD, Doin JE, Tate AL, & Slocum GH (1992) “Compression Stress Relaxation I, An Important Test For Evaluation of Sealant Materials”, Society of Automotive Engineers Standard, 920135. Busfield JJC & Thomas AG (2001) “Using FEA techniques to predict failure in elastomers”, Service Life Prediction of Elastomer Components, Institute of Materials, 15 October, London, UK. Cadge D & Prior A (1999) “Finite element modelling of three-dimensional elastomeric components” in

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Elastomers and Components: Service Life Prediction – Progress and Challenges Finite Element Analysis of Elastomers, D Boast and VA Coveney (eds), Professional Engineering Publishing, London, ISBN 1860581714, 187-205.

Chapman AV & Porter M (1988) “Sulphur vulcanization chemistry”, Chapter 12 in Natural Rubber Science and Technology, AD Roberts (ed), Oxford University Press, 511-620. Coveney VA & Menger C (1999) “Initiation and Development of Wear of an Elastomeric Surface by a Blade Abrader”, Wear 233-235, 702-711. Coveney VA & Menger C (2000) “Behaviour of Model Abrasive Particles Between a Sliding Elastomer surface and a Steel Interface”, Wear 240, 72-79. Coveney VA & Rizk R (2005) “Life prediction of O-rings used to seal gases” (This Volume). Daley JR & Phillips HM (2000) “Cost-effective perfluoroelastomer sealing solutions for aggressive environments”, Proceedings of the 16th International Fluid Sealing Conference, Brugge, 18-20 September, R Flitney (ed), Professional Engineering Publishing, ISBN 1860582540, 135-146. Daley JR & Mays S (1999) “The Complexity of Material Modelling in the Design Optimisation of Elastomeric Seals”, in Finite Element Analysis of Elastomers, D Boast and VA Coveney (eds), Professional Engineering Publishing, London, ISBN 1860581714, 119-128. Eason RJH & Barnes N (1994) “Seals and Sealing”, Chapter 15 Section 2 in Mechanical Engineers Reference Book, EH Smith (ed), Butterworth-Heinemann, Oxford, 15-18 & 15/75. Ferry JD (1992) “Elastomers: dynamic mechanical properties” in Concise Encyclopaedia of Polymer Processing and Applications, PJ Corish (ed), Pergamon, Oxford, 252-256. Fuller KNG (1988) “Rheology of raw rubber”, Chapter 5 in Natural Rubber Science and Technology, AD Roberts (ed), Oxford University Press, 141-176. Gough J, Gregory IH & Muhr AH (1999) “Determination of constitutive equations for vulcanized rubber” in Finite Element Analysis of Elastomers, D Boast and VA Coveney (eds), Professional Engineering Publishing, London, ISBN 1860581714, 5-26. Hertz DL (1992) “Introduction”, Chapter 1 in Engineering with Rubber – How to Design Rubber Components, AN Gent (ed), Hauser, Munich, 1-9. Ho E & Nau BS (1996) “Gas emission by permeation through elastomeric seals”, Tribology Transactions, 39 (1), 180-186. Huy ML & Evrard G (2000) “Methodologies for lifetime predictions of rubber using Arrhenius and WLF models”, Lifetime estimation of rubber materials by ageing and stress relaxation tests, 31 October, Sweden. ISO 2921 (1997) “Rubber, vulcanized – determination of low temperature characteristics – temperatureretraction procedure (TR test)”, International Standards Organisation. Menger C (2001) “Behaviour of sliding seals in abrasive fluids”, PhD Thesis, University of the West of England, Bristol, UK. Morgan GJ, Campion RP & Derham CJ (2005) “Stress-induced phenomena in elastomers and their influence on design and performance” (This Volume). Spetz G (2000) “Stress Relaxation – Test methods, instruments and lifetime estimation”, Proceedings of Elastocon Conference, Sweden, 31 Oct-1 Nov. Stevens RD (2000) “Permeation and Stress Relaxation Testing of Fuel Seal Materials – A Comparison of Fuel System Elastomers”, RAPRA Conference Birmingham, UK, May. Stevenson A & Campion RP (1992) “Durability”, Chapter 7 in Engineering with Rubber – How to Design Rubber Components, AN Gent (ed), Hauser, Munich, 169-207.

CHAPTER 5

Parameter Dependence of the Fatigue Life of Elastomers F Abraham and T Alshuth Deutsches Institut für Kautschuktechnologie eV (DIK), Hannover, Germany S Jerrams Dublin Institute of Technology (DIT), Dublin, Ireland

SYNOPSIS Fatigue tests on ethylene propylene (EPDM) and styrene-butadiene (SBR) rubber revealed physical behaviour that is not seen in stiffer less extensible materials. Uniaxial cyclic tests, using cylindrical dumbbell testpieces, with the same minimum stress of zero (smin = 0) and varying stress amplitude (sa), predictably gave decreased fatigue life with increased stress amplitude and hence maximum stress (smax). However, tensile uniaxial cyclic tests where smin was increased in successive tests whilst the stress (sa) remained constant, produced longer fatigue lives for higher values of smax. EPDM and SBR materials were chosen for the tests because they do not strain crystallise during deformation and consequently this phenomenon has no influence. The results show that for smax cannot be used as a criterion to predict fatigue life of non-strain crystallising elastomers which are filled. An evaluation of recorded data of stress against strain gave evidence that energies control the fatigue life rather than stress and strain. However, what role the dissipated energy plays remains an open question. Experimental results on filled and unfilled rubber materials are evaluated and discussed.

1 INTRODUCTION Although elastomeric materials exhibit very high strains for relatively small stresses, making them appropriate for many automotive applications, they still have behaviour in common with other materials. In particular they have a limiting strength and tend to fatigue. Mechanical fatigue of elastomers is manifested in a progressive reduction of physical properties as a result of crack propagation during continuous dynamic excitation. Well-founded research into metals (Schwalbe, 1980; Bergmann et al, 1988) has shown that 59

60


fatigue results from atomic processes. Similar research for elastomers is at an early stage, because of the complex interaction between polymers, fillers, softeners and other additives. Currently predictions of the fatigue properties of elastomeric materials and components are predominantly of an empirical nature. Though there are levels of stress or strain below which elastomers will not suffer fatigue damage, such limits are not well established. There are very few examples of Wöhler curves (Wöhler, 1870) in the literature for rubbers due to the inordinate amount of time required to collect the data. Hence a precise knowledge of the durability of elastomers (rubbery materials) does not exist. Despite the increasing use of finite element analysis (FEA), producing durable rubber automotive components remains a challenge. The question of establishing a single parameter for elastomeric fatigue is unresolved. Arguments have been made that fatigue life is dependent on stress, strain and also strain energy density (Inglis, 1913; Irwin, 1948). When characterising crack propagation and fatigue properties, there are two problems unique to elastomers that must be surmounted for a computer simulation to successfully model fatigue. (i) Fatigue properties of elastomers are not only dependent on the basic chemical composition of the polymer, but also on individual considerations like the particular cross-linking system and the ageing protection used. (ii) As a result of their visco-hyperelastic properties, the behaviour of elastomers is sensitive to the application of different loading modes, stress amplitudes, strain amplitudes, frequencies, strain rates, waveforms and temperatures. Each of these problems emphasises the importance of optimising material models so that they represent the physical behaviour experienced by a component in service. Additionally, component testing must realistically represent in-service behaviour to allow accurate determination of fatigue characteristics.

2 OBJECTIVE The fatigue behaviour of materials like metals and ceramics is well researched and described in the literature. In particular, emphasis has been placed on the testing of fatigue properties with varying stress amplitudes and minimum stresses and this data has been represented on Wöhler curves and Haigh diagrams. Few studies have been carried out on the fatigue of elastomers and most of these have used natural rubber (NR). The influence of minimum stress and stress amplitude on the fatigue resistance of NR has been studied by André et al (1999) and Haigh-diagrams were used to display the data. Service life was shown to increase as minimum stresses increased from zero, for a single constant stress amplitude. The improved fatigue resistance with increased minimum and hence maximum stresses was described previously by Gent (1994) and attributed to the strain crystallisation of NR inhibiting crack growth. Previous studies carried out by the Deutsches Institut für Kautschuktechnologie (DIK) also showed an increase in fatigue life and a reduction of crack propagation with increases in minimum stress for non strain-crystallising rubber (Abraham et al, 2001a, 2001b, 2002; Abraham, 2002; Alshuth et al, 2002). The main objective of this work is the characterisation of the dependence of fatigue on stress amplitude and minimum stress in non strain-crystallising elastomers. Additionally, it

Parameter Dependence of the Fatigue Life

61

Fig. 1 Diagrammatic representation of cylindrical rubber dumbbell testpiece.

was considered necessary to include materials with and without filler in the investigation. This permits simultaneous studies on the effects of reinforcement and stress softening of filled systems. A second objective is to clarify the question of which parameter (stress, strain or energy) best characterises the fatigue properties of elastomeric materials. Reliable predictions of the service life of dynamically loaded components, using fracture mechanics concepts as well as FEA, depend entirely on the use of appropriate parameters and characterisation.

3 METHODS AND MATERIALS Unfilled and filled ethylene propylene terpolymer (EPDM) and styrene butadiene polymer (SBR) vulcanisates have been used in this research programme. The unfilled EPDM elastomer contained standard trade EPDM Buna EP G5450 and an accelerated sulphur cross-linking system. In the case of the filled EPDM 110 phr (70 phr, parts per hundred by weight of rubber, N550 and 40 phr N772) low activity carbon black and 70 phr softener oil were added. The unfilled SBR elastomer was composed of an oil extended standard trade SBR (SBR 1712) and an accelerated sulphur crosslinking system. The addition of 70 phr of high activity carbon black (N234) resulted in an SBR tyre tread elastomer. The experiments used dumbbell testpieces of 25mm free length and 15mm diameter as shown in Figure 1. The diameter of the ends is 25mm with a 5mm fillet radius between major and minor diameters. This testpiece is capable of being cycled in tension and compression under uniaxial loading. Dynamic fatigue tests were carried out with a servohydraulic test system (MTS 831.50) at room temperature and with force varying sinusoidally at a frequency of 1Hz. The frequency was chosen to induce failure due to the initiation and growth of cracks without large increases in temperature and consequent thermal breakdown (Seldén, 1995). The tests were load controlled (engineering stress controlled) to failure and at least three testpieces

62

Elastomers and Components: Service Life Prediction – Progress and Challenges 700 300N load range, zero minimum load 400N load range, zero minimum load 500N load range, zero minimum load 600N load range, zero minimum load

600 500

Load in N

400 300 200 100 0 – 100 –5

0

5

10

15 20 25 Displacement in mm

30

35

40

Fig. 2 Diagram of four test conditions to generate Wöhler curves (zero minimum load) for filled EPDM.

per test procedure were used to provide sufficient data. (Usually 5 or more test specimens were used to give an average value.) During the fatigue tests, modulus and loss factor (evaluated by sine regression method) and full hysteresis loops were recorded for later analysis. Since the tests were performed under load control, displacements (and strains)

700 0N minimum load, 400N load range 100N minimum load, 400N load range 200N minimum load, 400N load range

600

Load in N

500 400 300 200 100 0 –100 0

5

10

15

20 25 30 Displacement in mm

35

40

45

Fig. 3 Plots of load against displacement for one fixed load range (400N) but three different minimum loads, for filled EPDM.


63

Log10 max. eng. stress in MPa

0.2

0.1

0

– 0.1 zero minimum load, load range variation 180N load range, minimum load variation – 0.2

0

1

2 3 4 Log10 fatigue life in cycles

5

6

Fig. 4 Log10 of the maximum engineering (nominal) stress against log10 of number of cycles to failure for unfilled EPDM for various load ranges and minimum loads.

varied during the tests; the variations were appreciable in the case of the filled materials. Therefore, in calculating the strain “range” (double amplitude of strain, see below) displacement values averaged throughout each test were used. All unfilled and filled EPDM and SBR materials were tested under various loading conditions. Two different test procedures were used. Procedure 1 used tests with a minimum load of zero and a range of different load amplitudes (Figure 2). Procedure 2 included tests with constant load amplitudes and different minimum loads (Figure 3). The tests with a zero minimum load represent an approximate full relaxation condition, as would occur under pulse loading. In the case of the series with variation of the minimum load, no full relaxation is allowed. Changes in maximum load (stress) resulted from varying load amplitude and minimum load. This allowed and therefore the influence of maximum stress, as a parameter for determining fatigue life, to be studied.

4 RESULTS 4.1 FATIGUE

The results of the fatigue tests on the unfilled EPDM are plotted in Figures 4 to 6. Figure 4 shows the well-known dependence of fatigue life on maximum stress (S-N curve or Wöhler-curve). All tests were to total failure of the test specimen. It appears to be unimportant whether the maximum stress is attained in conjunction with a large or small stress amplitude. Relaxing and non relaxing test conditions lead to an identical relationship between maximum load and fatigue life. For unfilled EPDM the results show that maximum stress can be used as a parameter for life prediction.

64


Log10 strain range in %

2.2

2

1.8

1.6 zero minimum load, load range variation 180N load range, minimum load variation 1.4

0

1


5

6

Fig. 5 Log10 of the strain range against log10 of number of cycles to failure for unfilled EPDM for various load ranges and minimum loads.

Figure 5 shows the relationship between fatigue life (n) and cyclic strain “range” for unfilled EPDM; it is clear that a single relationship exists between strain “range” and n, irrespective of the value of the cyclic stress minimum. Hence the cyclic strain “range” could also be used as a parameter for fatigue life prediction for the unfilled EPDM. The tests also confirm that the dependence of fatigue life on dynamic strain energy is independent of the adjusted test parameters minimum stress and stress amplitude. The

Log10 max. dyn. stored energy in Nmm

4

3.5

3

zero minimum load, load range variation 180N load range, minimum load variation 2.5 0

1


5

6

Fig. 6 Fatigue properties of unfilled EPDM (energy dependency). Log10 of the maximum dynamic stored energy against log10 of number of cycles to failure for various load “ranges” and minimum loads.


65


0.8

0.6

0.4

0.2

0

zero minimum load, load range variation 400N load range, minimum load variation 500N load range, minimum load variation 2

3

4 Log10 fatigue life in cycles

5

6

Fig. 7 Log10 of the maximum engineering (nominal) stress against log10 of number of cycles to failure for filled EPDM for various load “ranges” and minimum loads.

results provide a single curve for the unfilled EPDM relating the dynamic strain energy to fatigue life (Figure 6). Consideration of the detailed testing or operating conditions is shown to be unnecessary for a precise prediction of fatigue life. The behaviour of the filled EPDM differs fundamentally from that of the unfilled material (Figures 7 to 9). If the minimum stress is kept at zero while the stress amplitude is varied, the fatigue life


2.2

2

1.8 zero minimum load, load range variation 400N load range, minimum load variation 500N load range, minimum load variation 1.6 2

3


5

6

Fig. 8 Log10 of the strain range against log10 of number of cycles to failure for filled EPDM for various load “ranges” and minimum loads.

66



4

3.5

3 zero minimum load, load range variation 400N load range, minimum load variation 500N load range, minimum load variation 2.5 2

3


5

6

Fig. 9 Log10 of the maximum dynamic stored energy against log10 of number of cycles to failure for filled EPDM for various load “ranges” and minimum loads.

decreases as the maximum stress increases, as shown in Figure 7. However, when the maximum stress is increased whilst a constant stress amplitude is maintained, fatigue life or number of cycles to failure increases despite an increase in maximum stress. Figure 7 shows that the same maximum stress for different stress amplitudes results in very different fatigue lives. In this case maximum stress is not a useful parameter for fatigue life prediction. Indeed, results from the tests show that under certain conditions an increase in maximum stress in filled EPDM can lead to an increase of the service life, in terms of cycles to failure, by a factor of more than 10.


–0.2

–0.3

–0.4

zero minimum load, load range variation 80N load range, minimum load variation –0.5 2

3


5

6

Fig. 10 Log10 of the maximum engineering (nominal) stress against log10 of number of cycles to failure for unfilled SBR for various load “ranges” and minimum loads.


67


2.3

2.1

1.9

zero minimum load, load range variation 80N load stroke, minimum load variation 1.7 2

3


5

6

Fig. 11 Log10 of the strain range against log10 of number of cycles to failure for unfilled SBR for various load “ranges” and minimum loads.

Figure 8 shows the effect on the relationship between cyclic strain range and life achieved by varying the load amplitude for zero minimum load. The effect is seen to follow a similar pattern (Wöhler curve) to that observed for the relationship between life and stress amplitude (q.v. Figure 7). However, when the minimum load in the cycle is also varied it is found that no single curve defines the relationship between fatigue life and strain “range”. Thus strain “range” (double amplitude of strain) is an inappropriate parameter for predicting the fatigue life of filled EPDM.


3.5

3.2

2.9

zero minimum load, load range variation 80N load range, minimum load variation 2.6 2

3


5

6

Fig. 12 Log10 of the maximum dynamic energy against log10 of number of cycles to failure for unfilled SBR for various load “ranges” and minimum loads.

68



0.4

0.2

0 zero minimum load, load range variation 300N load range, minimum load variation 240N load range, minimum load variation

– 0.2

3

4 5 Log10 fatigue life in cycles

6

Fig. 13 Log10 of the maximum engineering (nominal) stress against log10 of number of cycles to failure for filled SBR for various load “ranges” and minimum loads.

Figure 9 shows the correlation between maximum dynamic stored energy and fatigue for the filled EPDM material. A single curve results when varying both the minimum stress and the stress amplitude. This suggests that maximum dynamic stored energy is a promising parameter for fatigue life in components made from (unfilled or filled) EPDM, irrespective of the loading conditions. This finding may be consistent with the concept that crack growth depends on the strain energy released during cycling (Griffith, 1920; Rivlin & Thomas, 1953; Lake & Lindley, 1964, 1965; Lake, 1983; Lake & Thomas, 1988; Busfield & Ng, 2005; Muhr 2005).


2.3

2

1.7 zero minimum load, load range variation 300N load range, minimum load variation 240N load range, minimum load variation 1.4 3


6

Fig. 14 Log10 of the strain range against log10 of number of cycles to failure for filled SBR for various load “ranges” and minimum loads.


69


4

3.6

3.2

2.8

zero minimum load, load range variation 300N load range, minimum load variation 240N load range, minimum load variation

2.4 3


6

Fig. 15 Log10 of the maximum dynamic energy against log10 of number of cycles to failure for filled SBR for various load “ranges” and minimum loads.

The behaviour of the SBR elastomers is shown in Figures 10 to 15. For unfilled SBR, as was the case for unfilled EPDM, minimum stress has no influence on the relationships between fatigue life and the following parameters: maximum stress, strain “range” and maximum dynamic stored energy. All three parameters appear appropriate for fatigue life prediction (Figures 10 to 12). In some tests the carbon black filled SBR (tyre tread) elastomer shows an increase in 500 cycle 6 cycle 202 cycle 7449 cycle 7645

Load in N

400

fatigue life 7709 cycles (1Hz)

300

200

100

0 0

20

40

60

80 100 Strain in %

120

140

160

Fig. 16 Hysteresis loops of a filled EPDM testpiece during fatigue testing at a load range of 400N with zero minimum load (load control, 1Hz). Fatigue life was 7709 cycles.

70

Elastomers and Components: Service Life Prediction – Progress and Challenges 0.5

2.6

2.2

0.4

1.8

0.3

E″ in N/mm2

E′ in N/mm2

E′ E

fatigue life 7709 cycles 0N – 400N, load control, 1Hz 1.4

1

10

100 Number of cycles

0.2 10000

1000

Fig. 17 Storage (E′) and loss (E′′) “moduli” for filled EPDM plotted against number of sinusoidal cycles at a load “range” of 400N with zero minimum load. (Load control, 1Hz.) Fatigue life was 7709 cycles.

fatigue life by a factor of 10 when increasing the minimum load. As for filled EPDM, maximum stress is found to be an inappropriate parameter for determining fatigue life. However, the maximum stored energy is again seen to provide a basis for predicting cycles to failure (Figures 13-15). It is clear from the results for filled EPDM and filled SBR, that maximum stress can be a very misleading parameter in respect of fatigue life prediction (Figures 7 and 13). Energy

2.5

0.2 E* tan delta

E* in N/mm2

0.15

2

Tan delta

0.1.75

2.25

0.125

1.75 fatigue life 7709 cycles 0N – 400N, load control, 1Hz 1.5 1

10


1000

0.1 10000

Fig. 18 Complex modulus (magnitude, E*) and loss factor (tanδ) for filled EPDM plotted against number of sinusoidal load cycles (n) at a load “range” of 400N with zero minimum load. (Load control, 1Hz.) Fatigue life was 7709 cycles.

Parameter Dependence of the Fatigue Life 1300

Strain Dissipated Energy

140

1200

120

1100

100

1000

Dissipated energy in N/mm

Strain range in %

160

71

fatigue life 7709 cycles 0N – 400N, load control, 1Hz 80 1

10


1000

900 10000

Fig. 19 Strain “range” and dissipated energy per cycle for filled EPDM plotted against the number of sinusoidal load cycles at a load “range” of 400N with zero minimum load (load control, 1Hz). Fatigue life was 7709 cycles.

criteria give a single curve, but small systematic deviations are observed from the normal S-N curves when a non zero minimum stress is applied (Figure 9 and 15). 4.2 CHANGES IN PHYSICAL PROPERTIES DURING THE TEST

The data from all the tests show that the filled EPDM undergoes changes in physical properties during the load controlled cycles. The dynamic displacement induces an increasing amount of set as each test progresses as shown in Figure 16. It is usual for the modulus of filled rubbers to decrease significantly during the first few cycles of a physical test as a result of stress softening (Mullins effect). However these fatigue tests show that the complex, storage and loss “moduli” (E*, E′, E′′ for the material as well as loss factor tanδ (all evaluated by the sine regression method) decrease throughout the test until fracture (Figures 17 and 18). The dissipated energy per cycle levels out after approximately 500 cycles – as shown in Figure 19 – as a consequence of the strain behaviour and the change in tanδ. It is worth noting that no visible cracks were observed until 7449 cycles were reached (penultimate recorded hysteresis loop in Figure 16) and complete rupture occurred within approximately 200 cycles (at 7709 cycles). The same phenomenon can be seen under less severe test conditions when test specimens fail after a few hundred thousand cycles. The tests show that for filled EPDM testpieces, failure is reached when the complex modulus E* has fallen to 76 % ± 5 % of the initial value irrespective of the test conditions. This may give a measure of stiffness loss at which a component manufactured from this material will fail. This finding potentially offers an important predictor for the maintenance and replacement of elastomeric components just prior to failure. Other materials will presumably fail at different values.

72

Elastomers and Components: Service Life Prediction – Progress and Challenges 5 SUMMARY

The experimental results of this work show that the fatigue properties of filled EPDM and SBR elastomers under equal conditions of temperature and frequency (etc) depend on the applied stress amplitude as well as minimum stress. Increasing minimum stress even with constant stress amplitude can increase the fatigue life by a factor greater than 10 despite the concurrent increase in maximum stress. These effects do not apply to unfilled rubbers investigated within this study. Because EPDM and SBR were used in the tests, strain crystallisation cannot explain the increases in fatigue life. It is evident that the phenomenon of increased fatigue life with increased maximum stress is related to the properties of the rubber filler system. The improvement of the fatigue properties with minimum stress variation can be used constructively to increase the service life of components, or put simply, pre-loading filled EPDM and SBR components increases their fatigue life. For filled EPDM and SBR, maximum load or stress as well as the strain “range” do not allow a basis for fatigue life prediction. In contrast, minimum load or stress appears not to influence the relationship between fatigue life and maximum dynamic stored energy (Umax). Thus maximum stress and strain “range” are not suitable parameters for fatigue life predictions. However, Umax does seem to be a promising parameter for these materials. Fatigue life prediction would, however, require accurate simulation of service conditions and would most probably involve the use of finite element analysis. It is planned to investigate the influence of viscoelasticity under sinusoidal loading at different frequencies and under pulse loading conditions. The next phase of the research will be a project on dynamic crack propagation under similar variation of minimum stresses and stress amplitudes. The dynamic stiffness (k*) (or dynamic “modulus” E*) and loss factor (tanδ) of the filled EPDM decreased throughout each fatigue test. In each loading case, for the filled EPDM failure was imminent when k* (E*) had fallen to approximately 76% of its initial value. This in turn suggests that a component made from this material will fail in fatigue when its stiffness has fallen to a given value, irrespective of the loading history. Determining similar values for other elastomers offers an opportunity to improve the maintenance and replacement of rubber components, provided that periodic measurement of the stiffness is carried out.

ACKNOWLEDGEMENT The Authors and the Deutsches Institut für Kautschuktechnologie eV (DIK) would like to thank the Deutsche Kautschuk-Gesellschaft eV (DKG) for supporting this work.

REFERENCES Abraham F (2002) “The influence of minimum stress on the fatigue life of non strain-crystallising elastomers”, PhD Thesis, Coventry University, December. Abraham F, Alshuth T & Jerrams S (2001a) “Ermüdungsbeständigkeit von Elastomeren – Einfluss der Spannungsamplitude und der Unterspannung”, Kautschuk Gummi Kunststoffe 54, 643-647. Abraham F, Alshuth T & Jerrams S (2001b) “The dependence on mean stress and stress amplitude of the fatigue life of EPDM elastomers”, Plastics, Rubber and Composites 30, 421-425.


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Abraham F, Alshuth T & Jerrams S (2002) “Ermüdungsbeständigkeit von Elastomeren – Einfluss der Spannungsamplitude und der Unterspannung Teil 2”, Kautschuk Gummi Kunststoffe 55, 674-678. Alshuth T, Abraham F & Jerrams S (2002) “Parameter dependence and prediction of fatigue life of elastomers products”, Rubber Chem Technol 75, 635-642. André N, Cailletaud G & Piques R (1999) “Haigh diagram for fatigue crack initiation prediction of natural rubber components”, Kautschuk Gummi Kunststoffe 52, 120-123. Bergmann JW, Heidenreich R, Bügler H & Oberparleiter W (1988) “Bauteilspezifische Werkstoffuntersuchungen 1986 (Werkstoffdaten zur Auslegung von Turbinenscheiben aus UDIMET 700 as HIP”, IABG-Bericht B-TF-2355. Busfield JJC & Ng WH (2005) “Using FEA techniques to predict fatigue failure in elastomers”, (This Volume). Gent AN (1994) “Strength of Elastomers”, Chapter 10 in Science and Technology of Rubber, Mark J E, Erman B& Eirich FR (eds), 2nd edition, Academic Press, 471-512. Griffith AA (1920) “The phenomena of rupture and flow in solids”, Philosophical Transactions of the Royal Society of London, Series A, 221, 163-198. Inglis CE (1913) “Stresses in a plate due to the presence of cracks and sharp corners”, Transactions of the Institute of Naval Architects, 55, 219-241. Irwin GR (1948) “Fracture dynamics, Fracturing of metals”, American Society for Metals 40, 147-166. Lake GJ (1983) “Aspects of fatigue and fracture of rubber”, Prog Rubber Technol, 45, 89-143. Lake GJ & Lindley PB (1964) “Ozone rracking, and fatigue of rubber. Part 1: Cut growth mechanisms and how they result in fatigue failure. Part 2: Technological aspects”, Rubber Journal, 146, (10), 24-30; 146, (11), 30-39. Lake GJ & Lindley PB (1965), “The mechanical fatigue limit for rubber, and the role of ozone in dynamic cut growth of rubber” Journal of Applied Polymer Science, 9, 1233-1251. Lake GJ & Thomas AG (1988) “Strength properties of rubber”, Chapter 15 in Natural Rubber Science and Technology, AD Roberts (ed), Oxford University Press, 731-772. Muhr AH (2005) “Fracture of rubber-steel laminated bearings”, (This Volume). Rivlin RS & Thomas AG (1953) “Rupture of rubber Part 1. Characteristic energy of tearing”, Journal of Polymer Science, 10, 291-318. Schwalbe K-H (1980), Bruchmechanik metallischer Werkstoffe, Carl Hanser Verlag ; München, Wien. Seldén R (1995) “Fracture mechanics analysis of fatigue of rubber – A review”, Progress in Rubber and Plastics Technology, 11, 56-83. Wöhler A (1870) “Über Festigkeitsversuche mit Eisen und Stahl”, Zeitschrift Bauwesen 20, 73-106.

CHAPTER 6

Strain Energy Release Rates for Some Classical Rubber Test Pieces by Finite Element Analysis OH Yeoh Lord Corporation, Erie, Pennsylvania, USA

SYNOPSIS Strain energy release rate or tearing energy has proven to be a valid failure criterion for a variety of rubber failure phenomena. However, apart from a small number of classical test pieces, it is difficult to calculate the tearing energy. This hampers the wider use of this criterion in failure analysis. As a benchmark exercise, finite element analysis is used here to compute the tearing energy for some classical rubber test pieces consisting of cracked strips and cylinders in tension. Results are used to reconcile some conflicts in the literature. Some guidance is given on choice of element types for such analyses.

1 INTRODUCTION Griffith (1921) proposed strain energy release rate as a failure criterion for fracture of glass. This eventually led to the development of the energetics approach in fracture mechanics. Rivlin & Thomas (1953) applied the Griffith failure criterion to the study of rubber tearing. Because of this first use of the Griffith criterion in rubber, strain energy release rate became known as tearing energy in the rubber literature. Since then, tearing energy has proven to be a valid failure criterion for a variety of rubber failure phenomena including tearing, fatigue crack growth, ozone cracking, adhesion, abrasion and cutting by sharp objects (Lake, 1995). However, in spite of its undoubted success as a unifying principle in explaining such a wide variety of rubber failure phenomena, tearing energy is not as commonly used in failure analysis or engineering design of rubber as one might expect. This is largely because of the difficulty in determining the tearing energy available. Large strain, non-linear elasticity problems are notoriously intractable except for simple geometries and loading conditions. Thus, the wider use of tearing energy in failure analysis of rubber is hampered. The advent of finite element analysis (FEA) and modern computers have allowed the solution of previously intractable large strain, non-linear elasticity problems. So, in 75

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principle at least, finite element analysis may be used to compute tearing energy. Indeed, the calculation of tearing energy was one of the first applications of the finite element method when its use for solving rubber problems was first advocated in the early 1970s (Lindley, 1972). Therefore, it is perhaps surprising to find that there are basic questions relating to classical rubber test pieces that can be readily addressed using finite element analysis, and yet remain unanswered. This chapter revisits some classical rubber test pieces consisting of cracked strips and cylinders in tension to address some of these questions as an exercise to benchmark modern finite element techniques.

2 THEORY The tearing energy, G, available for the propagation of a crack may be defined by (Rivlin & Thomas, 1953)

(1) where U is the total strain energy stored in the deformed rubber specimen (assumed to be perfectly elastic), and A is the area of one crack surface. The partial derivative is evaluated under constant displacement conditions so that external forces do no work. It should be noted that the negative sign implies that energy is released from the deformed specimen by crack growth, hence the alternative name for G, strain energy release rate (per unit area of crack surface formed). The SI units for G (sometimes written as T) are J/m2. 2.1 THIN STRIPS (PLANE STRESS)

The tearing energy available can be readily determined for simple geometries and loading conditions. In their classical paper, Rivlin & Thomas (1953) discussed two simple tensile specimens (a) a long, thin rubber strip with a small central crack perpendicular to the direction of loading and (b) a similar strip with a small edge crack. Preferring symmetry, which is convenient for FEA modelling, we paraphrase their analysis by considering the analogous problem of a long rubber strip with two small symmetric edge cracks in place of b). Figure 1 shows the two test pieces considered here. Note that the length of the central crack is 2c in the first test piece while the length of each symmetric crack is c in the second. Because of symmetry, it is only necessary to consider one half of each test piece. The tearing energy available for crack propagation can be determined from dimensional arguments. In the absence of cracks, the test piece is in a uniform state of simple extension. Therefore, the strain energy density (strain energy stored in unit volume of rubber) everywhere in the test piece is the same, say, W. When a small crack of length c is introduced in each half test piece, a volume of strained rubber in the vicinity of the crack is relaxed. This volume should scale according to c2. Therefore, the strain energy released is

Strain Energy Release Rates

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Fig. 1 Schematic sketch of test pieces (a) central crack (b) symmetric edge cracks.

also proportional to c2 and is given by

(2) where k is a numerical constant for a given state of strain and t is the thickness of the rubber. Equations (1) and (2) yield (3) Although the above argument and Equation (3) apply to both test pieces, the value of k for the two test pieces is not necessarily the same. Indeed, the values of k are known to be different from linear fracture mechanics solutions. For a small central crack in a long strip of width, 2a, under a tensile load, F, the stress intensity factor, k1, is given by (Benthem & Koiter, 1973)

(4) For the corresponding cases of a single edge crack or symmetric edge cracks, the relation is (Benthem and Koiter, 1973)

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(5) Thus, according to linear fracture mechanics, an edge crack and symmetric edge cracks are more severe than a central crack. The relation between k1 and G for a thin plate in plane stress is well-known (e.g. Corten, 1972) to be

(6) where E is the Young’s modulus. So, it can be readily shown that for a central crack

(7) while for edge cracks (8) It is seen that at small strains, when linear fracture mechanics theory is applicable, k is expected to be some 26% higher for edge cracks than for a central crack. The rubber fracture mechanics literature gives a different view. Greensmith (1963) carried out careful elasticity experiments on stretched rubber strips with edge cracks and found k to be a slowly decreasing function of the extension ratio, λ. k has a value of about 3 at small extensions decreasing to a value somewhat below 2 at 200% extension. Lindley (1972) studied the edge crack problem using finite element analysis and obtained results in good agreement with Greensmith’s experiments. He proposed the empirical relation

(9)

Based upon an approximate theoretical analysis of strips with central cracks, Lake (1970) proposed that k is related to strain by (10) This yields the classical value, π, for k for a strip with a central crack at small strains. The relations proposed by Greensmith, Lindley and Lake are not very different and it is common to adopt the simple relation (11)

as sufficiently accurate (Thomas, 1994). Thus, in the rubber literature, no distinction is usually


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made between central and edge cracks. However, the pedantic may point out that such smudging ignores the fact that Lake’s value for k for a central crack is actually higher than Greensmith’s and Lindley’s k for edge cracks when the reverse is predicted by linear fracture mechanics. This discrepancy between linear and non-linear fracture mechanics is investigated here. 2.2 THICK BLOCKS (PLANE STRAIN)

Most rubber test pieces are cut from thin sheets. Thus, deformation is essentially plane stress. However, practical rubber components are often large and deformation is closer to plane strain. If we considered plane strain test pieces, Figure 1 would represent thick blocks (thick in the direction perpendicular to the paper) and the cracks would have the shape of ribbons. The distinction between plane stress and plane strain is not often discussed in the rubber literature. In linear fracture mechanics (e.g. Benthem & Koiter, 1973; Corten, 1972) the stress intensity factor k1 is the same for plane stress and plane strain. The expressions for G have the same form as Equations (7) and (8). However, because the stored energy density, W, at a given nominal extension is different in plane stress and plane strain, the absolute value of G is correspondingly different. We investigate here whether there is a need to distinguish between plane stress and plane strain when large strains are involved. 2.3 CYLINDERS (AXISYMMETRY)

Similarly, if we considered axisymmetrical test pieces, Figures 1(a) and 1(b) would represent cylinders with an internal penny-shaped crack and an external ring crack, respectively. In these test configurations, the crack front dimension changes as the crack grows; increasing in the case of pennyshaped cracks and decreasing in the case of ring cracks. This is in contrast to cracks in thin sheets or thick blocks discussed above where the crack front dimension remains constant as the crack grows. Huang & Yeoh (1989) considered the case of a penny-shaped crack in a stretched cylinder. From dimensional considerations, they argued that the strain energy released by the introduction of a penny-shaped crack of radius, c, is given by

(12) and the corresponding expression for tearing energy is

(13) The linear fracture mechanics solution (Benthem & Koiter, 1973; Corten, 1972) for tearing energy is

(14) implying that k has a value of 4 at small strains. Huang & Yeoh (1989) assumed that k is independent of strain as a first approximation.

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Lindley (1972) used finite element analysis to consider the energy available for the propagation of a crack in the thin end of a wedge test piece. Since his results were relatively insensitive to the wedge angle, he suggested that they might also hold for a penny-shaped crack in a cylinder. He obtained an expression for tearing energy analogous to Equation (13) with k decreasing from a value of 5.45 at small strains to a value of about 2.93 at a strain of 150%. Lindley’s k is significantly higher than the linear fracture mechanics solution at small strains. Chang et al (1993) also studied the penny-shaped crack problem using finite element analysis. They reported a value of 4 for k at small strains in good agreement with linear fracture mechanics theory. They found k decreases with increasing strain but much less rapidly than suggested by Lindley (1972). They pointed out that the plane stress conditions assumed by Lindley in solving the wedge problem would not apply to a fully embedded penny-shaped crack. A dimensional analysis may also be performed on the ring crack problem. The presence of a small (shallow) ring crack of depth c in a cylinder of radius a allows a volume of material in the vicinity of the crack to relax. This volume of material should scale according to c2 so we may write (15) and (16) The expression for G has the same familiar form but we still need to evaluate k. From linear fracture mechanics (Benthem & Koiter, 1973; Corten, 1972) we find that k has a value of 2.96 at small strains. It is not obvious how k depends on strain in the case of ring cracks. 3 FEA PROCEDURES Most of the finite element analyses reported here were performed using ANSYS 5.2 (Ansys Inc USA). For linear FEA, eight-noded Plane82 elements were used. Poisson’s ratio was taken as 0.4995. Displacements corresponding to an overall extension of 1% were imposed on the appropriate nodes. Crack growth was simulated by releasing the displacement constraints at appropriate nodes one element at a time. For non-linear FEA, similar procedures were used to perform analyses at strains of 1, 5, 10, 20, 40, 60, 80 and 100%. Initially, eight-noded Hyper84 (displacement formulation) plane elements were used with reduced integration except in the case of plane stress where eight-noded Hyper86 brick elements were used. Subsequently, in version 5.7, ANSYS introduced additional element types. Some analyses were repeated using eight-noded Solid183 plane elements. A neoHookean material model was used. The model is defined by the strain energy function (17) where µ (sometimes written as G) is the shear modulus and I1 is the usual strain invariant of rubber elasticity (Rivlin, 1992). In the material model a bulk modulus (K) to µ ratio of 1000 (equivalent to a Poisson’s ratio of 0.4995 in linear FEA) was used.


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Fig. 2 Schematic diagram showing deformed 12 x 12 model. Linear FEA results for a thin strip subjected to 1 % extension. Note crack has been simulated by releasing constraints at nodes of five elements located at bottom left hand corner.

To compare results using a different finite element program, some analyses were performed using FLEXPAC, a code developed in an International Fatigue Life Research Project led by Materials Engineering Research Laboratory Ltd, UK and Mechanics Software Inc, USA. FLEXPAC uses eight-noded or nine-noded plane elements (hybrid displacement-pressure formulation) with 3x3 Gauss integration reformulated for slightly compressible hyperelastic materials. Analyses were performed with 12 x 12 graded mesh models (except where indicated otherwise) using two lines of symmetry. The linear dimensions of the largest elements were 8 times larger than the smallest. The smallest element was located at the corner of the model where the crack was to be simulated by release of the displacement constraints one element at a time. To illustrate details of the model, Figure 2 shows the deformed mesh for the particular case of a central crack five elements in length in a thin strip subjected to simple extension.

4 RESULTS AND DISCUSSION 4.1 PRELIMINARY RESULTS FROM LINEAR FEA

In order to establish that our FEA models were adequate, we performed some preliminary linear analyses for central cracks in thin test strips (plane stress). Figure 3 (solid circles, solid line) shows the energy released with crack growth in a 12 x 12 element model subjected to a tensile strain of 1%. It is seen that ∆U is proportional to c 2 as predicted by Equation (2) for cracks up to about 20% of the width. This is consistent with experimental observations of Rivlin & Thomas (1953) and Greensmith (1963). We


∆U/W

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Fig. 3 Decrease in strain energy due to the presence of cracks in a thin strip. Plane stress linear FEA results for 12 x12 model.

estimated k from the slope of line in Figure 3 and obtained a value of 2.95 which is 6.1% less than the theoretical value of π. The analysis was repeated with 24 x 24 element model graded in the same 8:1 manner. Similar results were obtained which yielded a value for k of 3.00 or 4.5% less than theory. Thus, increasing the mesh density by four times gave a result marginally closer to theory. It is noteworthy that our FEA results consistently underestimate k. This arises because ∆U is obtained by subtracting the stored energy in the cracked specimen from that in an uncracked specimen. The strain in the uncracked specimen is uniform. This is a trivial problem for FEA and the results are very accurate. On the other hand, the strain distribution in the cracked specimen is complex and results are only approximate. The finite element technique tends to overestimate the stored energy in the cracked specimen. This results in an underestimate of ∆U and, hence, k. The theoretical result from linear fracture mechanics applies to an infinitely long test piece. Our square model essentially ignores any energy changes in the rubber located at a distance farther than the half-width. This is an additional source of error. To investigate the effect of modelling a longer test piece, we repeated the analysis using a 12 x 24 mesh and a 12 x 48 mesh which are two and four times as long as the 12 x 12 mesh. These yielded values for k of 3.03 and 3.06 which are 3.6% and 2.6% less than π respectively. Clearly, modelling large specimens with a high mesh density is expected to yield results closer to theory but this is computationally expensive. We are forced to recognize that FEA is an approximate technique, and that there is a necessary compromise between effort and accuracy of results. For our present purposes, we chose to standardize on a 12 x 12 mesh for reasons of expediency. This relatively small model and coarse mesh appears adequate for illuminating general trends although absolute errors of the order of several percent must be expected.


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Fig. 4 Dependence of k on strain for cracks in a thin strip (plane stress). Non-linear FEA results with different element types.

Returning to Figure 3, we note that the results for symmetric edge cracks (open circles, broken line) are similar to those for a central crack; ∆U is proportional to c2 for crack lengths up to about 20% of the half-width, a. However, the slope of the line yields a value of 3.59 for k. This is significantly higher than that reported by Greensmith (1963) and Lindley (1972) and also higher than our FEA results for a central crack. But, considering that our FEA results for a 12 x 12 mesh are generally lower by several percent, it is quite consistent with linear fracture mechanics theory which predicts a value of 1.26π. 4.2 THIN STRIPS (PLANE STRESS)

To study the effect of large strains, non-linear FEA was performed on models of thin test strips with central and edge cracks. Because ANSYS Hyper84 plane elements do not support plane stress analysis, we performed 3D analyses using 12 x 12 x 1 eight-noded Hyper86 brick elements (reduced integration) with no constraints in the thickness direction. Subsequently, in version 5.7, ANSYS enhanced the versatility of their Solid18X family of elements making them suitable for modelling rubber. This allowed us to repeat the analysis using 12 x 12 Solid183 elements (2D plane stress option). The change in strain energy due to the presence of a crack was also found to be proportional to c2 for cracks up to 0.2a. k was found to be higher for edge cracks compared to central cracks. In both cases, k decreased with increasing strain. The dependence of k on strain is shown in Figure 4. Several features are noteworthy. First, estimates of k from Hyper86 brick elements at 1% strain are lower than the corresponding values from linear FEA. They are also lower than corresponding values from Solid183 elements for the entire strain range. This is probably due to the fact that Hyper86 are

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Fig. 5 Dependence of k on strain for cracks in a thick strip (plane strain) compared with corresponding results for a thin strip (plane stress).

linear (first-order) elements whereas Plane82 and Solid183 are quadratic (second-order) elements. Linear elements are often recommended for finite element analyses where elements become highly distorted and strain gradients are likely to be severe (Cadge & Prior, 1999). So, it seems they would be particularly suitable for crack problems in rubber. However, the results here show there is a disadvantage to linear elements. Having fewer degrees of freedom, linear elements tend to be stiffer than quadratic elements. This in turn leads to larger errors in ∆U and k. To compensate, it would be necessary to employ more linear elements. Second, k for edge cracks is higher than for central cracks at small strains. This is consistent with expectations from linear fracture mechanics. However, k for edge cracks falls faster with increasing strain. As a result, for strains in the practical range of 20-100%, differences in values of k are small. Thus, ignoring the difference between central and edge cracks in rubber is justifiable as an approximation. Third, the rate of decrease in k with λ follows approximately the λ-1/2 law suggested by Lake (1970) and Lindley (1972). Equation (11) is shown in Figure 4 for comparison. It is seen that Equation (11) is a reasonable approximation in the practical strain range of 20-100% [results from Solid183 elements (solid symbols) are deemed more accurate for reasons discussed above]. 4.3 THICK BLOCKS (PLANE STRAIN)

For a given nominal extension, λ, the strain energy density, W, is higher in plane strain compared to plane stress. For a neo-Hookean material, we can write W explicitly as

(plane stress)

(18)

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Log (∆U/W)


Fig. 6 Decrease in strain energy due to the presence of cracks in cylinders at 100% tension. Axisymmetric nonlinear FEA results.

and (plane strain)

(19)

This difference is, of course, reflected in the total strain energy and absolute tearing energy results from our FEA under plane strain deformation conditions using ANSYS Hyper84 (reduced integration) or Solid183 elements. However, once the difference in W has been accounted for, we focus on the dependence of k on strain. Figure 5 shows the dependence of k on strain for central and symmetric edge cracks for plane strain strips. Results for Hyper84 elements are shown. Very similar results were obtained using Solid183 plane strain elements but these have been omitted for clarity. Plane stress results have been reproduced from Figure 4 (solid symbols – Solid183 plane stress elements) for comparison. We note the following features: First, k values from plane strain and plane stress are equivalent; the small differences seen in Figure 5 are attributed to differences in element formulation between Hyper84 and Solid183 (for example, the elements have different number of integration points). At small strains, k for central and symmetric edge cracks have values consistent with π and 1.26π respectively from linear fracture mechanics theory (after taking into account the fact that our FEA results tend to underestimate k). However, over the practical strain range of 20-100%, values of k for central and symmetric edge cracks are quite similar. Second, the rate of decrease in k with λ follows approximately the λ-1/2 law. Equation (11) is seen to be a good approximation. We conclude that the same relations for tearing energy apply in plane strain and plane stress just as in linear fracture mechanics.

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Fig. 7 Dependence of k on strain for cylinder with penny-shaped crack. Axisymmetric non-linear FEA results.

4.4 CYLINDERS (AXISYMMETRIC)

Dimensional analysis predicts that the strain energy released by the presence of an internal penny-shaped is proportional to c3 while that due to an external ring crack is proportional to c2. Figure 6 shows typical non-linear FEA results for the change in strain energy due to the presence of cracks in a cylinder stretched to 100% plotted on logarithmic scales. Lines of slope 3 and 2 have been drawn through the results for penny-shaped and ring cracks respectively. Good agreement is found with the predictions from dimensional analysis. Similar results were obtained at intermediate strains. Figure 7 shows the dependence of k on strain for an internal penny-shaped crack from FEA using ANSYS and FLEXPAC. Also shown in the same figure are the results of Chang et al (1993) who used ADINA. While the three FEA programs gave slightly different results it is clear that the general trend is the same; k is a slowing decreasing function of strain. According to linear fracture mechanics, k has a value of 4 at small strains. The tendency for our FEA results to be underestimates is attributed to the small and simple models we are using. We note that ANSYS Hyper84 elements gave the lowest values for k and hence appear to be the least efficient. FLEXPAC 9-noded (Quad9) elements gave higher values for k than the corresponding 8-noded element indicating the advantage of the extra node. It is noteworthy that Chang et al (1993) also used 9noded elements. The solid line shown in Figure 7 is the empirical relation (20)


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Fig. 8 Dependence of k on strain for cylinder with ring crack. Axisymmetric non-linear FEA results.

which appears to be a good approximation to the results after taking into consideration our tendency to underestimate k. This means that k decreases more slowly with strain than reported by Lindley. So, we agree with Chang et al (1993) that Lindley’s results are not applicable to internal penny-shaped cracks. Figure 8 shows the dependence of k on strain for an external ring crack from FEA using ANSYS and FLEXPAC. Again, the three element types gave slightly different results but the general trend is the same. At small strains, the expected value of k from linear fracture mechanics is 2.96. Again, our FEA results are underestimates. The error is somewhat larger than previously. This probably reflects the need for a much finer mesh in the vicinity of the outer surface of the cylinder since 2D axisymmetrical elements located there represent a much larger volume than elements located at the centre. The solid line in Figure 8 is the empirical relation (21) which reflects the general trend.

5 CONCLUSIONS Finite element analysis is a powerful tool for calculating tearing energy. Good insight into the mechanics of fracture is possible with relatively little effort using small models and coarse meshes. More exact solutions require significantly more effort. Experience with

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FEA on benchmark problems, such as discussed here, is important to guide decisions on how much effort should be expended on any specific problem. We found that the same tearing energy relation, G = 2kWc, which may be readily derived from dimensional considerations, apply to central and edge cracks in thin strips and thick strips in tension and to penny-shaped and ring cracks in cylinders in tension. However, k varies. At small strains, the values of k from FEA are consistent with linear fracture mechanics solutions. At large strains, k is a slowly decreasing function of λ. For cracks in thin strips (plane stress) and thick strips (plain strain) and ring cracks in cylinders k varies approximately as λ-1/2. For pennyshaped cracks, k decreases more slowly, varying approximately with λ-1/3. However, it should be noted that these dependences of k on strain where obtained using a neo-Hookean material model. Recent work documented in a separate paper (Yeoh, 2002) discussed differences arising from the use of different hyper-elastic material models.

ACKNOWLEDGMENTS Helpful discussions with MD Janowski and assistance from MA Smialowski are gratefully acknowledged. Based upon paper no. 2 presented at the 154th Meeting of the Rubber Division, American Chemical Society, Nashville, Tennessee, September 29-October 2, 1998.

REFERENCES Benthem JP & Koiter WT (1973) “Asymptotic approximations to crack problems”, Mechanics of Fracture – I – Methods of Analysis and Solutions to Crack Problems, GC Sih (ed) Noordhoff, Leyden, 131-178. Cadge D & Prior A (1999) “Finite element modelling of three-dimensional elastomeric components” in Finite Element Analysis of Elastomers, D Boast & VA Coveney (eds), Professional Engineering Publishing, 187-205. Chang YW, Gent AN & Padovan J (1993) “Strain energy release rates for internal cracks in rubber blocks”, Intl J Fracture, 60, 363-371. Corten HT (1972) “Fracture mechanics of composites”, Fracture – An Advance Treatise, Vol VII, H Liebowitz (ed), Academic Press, 676-769. Greensmith HW (1963) “Rupture of rubber. Part 10. The change in stored energy on making a small cut in a test piece held in simple extension”, J Appl Polym Sci, 7, 993-1002. Griffith AA (1921) “The phenomena of rupture and flow in solids”, Phil Trans Roy Soc, A221, 163-197. Huang YS & Yeoh OH (1989) “Crack initiation and propagation in model cord-rubber composites”, Rubber Chem Technol, 62, 709-731. Lake G J (1995) “Fatigue and fracture of elastomers”, Rubber Chem Technol, 68, 435-460. Lake GJ (1970) “Application of fracture mechanics to failure in rubber articles with particular reference to groove cracking in tyres”, Intl Conf Yield, Deformation and Fracture of Polymers, Cambridge. Lindley PB (1972) “Energy for crack growth in model rubber components”, J Strain Analysis, 7, 132-140.


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Rivlin RS (1992) “The elasticity of rubber” Rubber Chem Technol, 65, G51-66. Rivlin RS & Thomas AG (1953) “Rupture of rubber. Part 1. Characteristic energy for tearing”, J Polym Sci, 10, 291-318. Thomas AG (1994) “The development of fracture mechanics for elastomers”, Rubber Chem Technol, 67(3), G50-60. Yeoh OH (2002) “Relation between crack surface displacements and strain energy release rate in thin rubber sheets”, Mechanics of Materials, 34, 459-474.

CHAPTER 7

Heuristic Approach for Approximating Energy Release Rates of Small Cracks Under Finite Strain, Multiaxial Loading WV Mars Cooper Tire & Rubber Company, Findlay, Ohio, USA

SYNOPSIS In this chapter, a parameter is presented that attempts approximately to describe the energy release rate of a small crack of arbitrary orientation under multiaxial loading. The parameter, herein called the cracking energy density, specifically attempts to address several aspects common to the analysis of fatigue in rubber: finite straining, nonlinear elasticity, and the possibility of crack closure under compressive loading. As motivation, the connection between the strain energy density and the energy release rate for small cracks under uniaxial loading is first discussed. Small strain and finite strain definitions of the cracking energy density are then presented. The accuracy of the cracking energy density as an approximation of the energy release rate at small strains is assessed via comparison with results from linear elastic fracture mechanics (LEFM). The cracking energy density is shown to exhibit dependence on crack orientation and stretch biaxiality that resembles that predicted via LEFM. Since the cracking energy density is evaluated at a material point in the uncracked material, this parameter is particularly useful for the analysis of crack nucleation from initially unobserved flaws, a common task in the design of rubber components. In such applications, it is possible to predict not only a fatigue crack nucleation life, but also specific planes on which cracks would be expected to appear.

1 INTRODUCTION Two distinct approaches may be employed to rationalise fatigue failures involving the growth of small flaws under the action of mechanical forces. Crack nucleation approaches focus upon continuum mechanical quantities that are defined at a material point (i.e. strainor stress-based theories), and which traditionally have made no explicit consideration of the mechanics of flaw growth. Fracture mechanics approaches focus on characterising the local conditions at a crack tip, using quantities defined for a given crack (i.e. theories based on energy release rate or crack opening displacement). 91

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Fig. 1 Crack emanating from a naturally occurring void on a failed rubber specimen surface.

Usually, a new rubber component contains no plainly visible cracks or defects. After many cycles, however, visible fatigue cracks form due to the growth of unobserved flaws, which were present in the virgin material. The initial flaws typically have lengths in the range of 0.01-0.1 mm. Figure 1 illustrates crack growth from a void on the surface of a filled natural rubber specimen. Presumably, the void was present in the specimen prior to the application of any loading. After the initiation of a crack due to mechanical fatigue, the crack continues to grow until component failure ensues. It is useful to think of the crack history in two distinct phases, which may be distinguished by how the energy release rate varies with crack size. For cracks that are sufficiently small relative to other geometric features of a given specimen (so that far-field gradients of strain/stress have little influence), the energy release rate varies proportionally with crack length. The energy release rate depends also on the state of loading remote from the crack, and may be computed independent of the geometry of the component, using the far-field strain or stress. For larger cracks (where gradients may not be neglected, and where no clear far-field can be delineated), the energy release rate depends strongly on component geometry, and ceases to follow the original proportionality with crack length. Often, the number of cycles corresponding to the first phase of crack growth is more important than the number of cycles corresponding to the second. Note that the first phase always occurs before component failure, while the second phase may or may not occur (as small initiated cracks may be sufficient to cause component failure due to drop in stiffness). A designer may therefore regard the prevention of crack nucleation as a primary design goal. Consequently, understanding the behaviour of small cracks under complex loading and identifying reliable approaches for design analysis of small cracks are of great importance.

Heuristic Approach for Approximating Energy

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Both crack nucleation and fracture mechanics approaches have been developed and used for uniaxial life predictions in rubber. A review of these analysis approaches is given by Mars and Fatemi (2002). The fracture mechanics approach has been developed and applied with some success in multiaxial situations. Crack nucleation approaches have received less attention, and a theory adequate for predicting crack nucleation life under the action of a general multiaxial strain history is needed. This article describes a new theory for fatigue analysis of highly deformable, elastic materials under multiaxial loading. The theory links the strain state at a material point in an uncracked medium to a heuristic approximation of the energy release rate of an assumed pre-existing flaw embedded in the medium. This is accomplished through a parameter, the cracking energy density, which has been introduced previously for small strains (Mars, 2001). Qualitatively, the cracking energy density represents the portion of the total elastic strain energy density that is available to be released on a given material plane. The theory defines an analysis approach which can be used to predict both the initiation life and the material plane(s) on which failure initiates for a given strain history. As a preliminary to the theory it is shown that, in simple tension, the energy release rate is proportional to strain energy density and crack size. Reasons why this proportionality does not apply generally are then discussed. This is followed by a brief introduction to the concept of cracking energy density, based on small-strain theory. A finite strain formulation of cracking energy density is then given, along with discussions on accounting for crack closure, and on prediction of the crack initiation plane. Experimental results relating to the ability of the theory to rationalize multiaxial fatigue data are given by Mars & Fatemi (2001) and Mars (2002).

2 ENERGY RELEASE RATE OF SMALL CRACKS UNDER SIMPLE TENSION For small cracks under far-field simple tension loading, the energy release rate T (Lake & Thomas, 1988; Chang et al, 1993) may be expressed as a product involving the far-field strain energy density W and the crack size a, i.e. T = C W a, where C is a nondimensional factor. By small, it is meant that the stress/strain fields in the neighbourhood of the crack may be regarded as uninfluenced by the presence of any boundaries or far-field gradients. With this factorisation, C depends on the particular geometry of the crack (embedded penny crack, through-crack in a sheet, edge crack, etc). Of course, the factorisation is dimensionally consistent (Energy / Area = Energy / Volume x Length). Importantly, it relates a fracture mechanics parameter, the energy release rate, directly to a far-field continuum mechanical parameter, the strain energy density. When applying the factorisation T = C W a for multiaxial stress states and finite strains, C depends additionally on strain magnitude, constitutive behavior (Chang et al, 1993), and mode of deformation (Yeoh, 2002). The dependence of C on mode of deformation for this factorisation is shown below to be associated with the fact that, under multiaxial loading, not all of the far-field strain energy can be made available for release due to crack growth. Herein, an alternative factorisation is offered, T = C Wc a, where Wc is termed the cracking energy density, and C is again a (different) nondimensional factor. This quantity is introduced with the intent to permit, at least approximately, C to be regarded as independent of the mode of deformation (i.e. simple tension vs. equi-biaxial tension, for example) remote from the crack.

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Fig. 2 Schematic load distribution for a penny crack in an infinite medium under remote simple tension.

2.1 RELATIONSHIP OF THE STRAIN ENERGY DENSITY TO THE ENERGY RELEASE RATE

Consider an axisymmetric, penny-shaped crack, embedded in an infinite medium that is loaded in simple tension, as shown in Figure 2. The material surrounding the crack may be divided into three regions. Remote from the crack, denoted region 1, the strain energy density W1 is nonzero and constant. Near the crack faces, but away from the crack tip, region 0, the material is essentially relieved and the strain energy density is negligible. In the immediate vicinity of the crack tip, region 2, the average strain energy density W2 is magnified relative to the far-field value. Assuming that the only independent length dimensions that enter the calculation of W2 are the size a of the crack, and the size d of the region over which the average crack tip energy density is taken, dimensional arguments (e.g. the Buckingham Pi theorem) lead to the conclusion that, for fixed far-field loading, and a given ratio of d/a, the value W2 must remain constant, i.e. W2 = K1W1. Of course, a given value of d/a implies that the size of each region scales with the size of the crack. The energy release rate of the crack may be computed from the definition T= (see Azura & Thomas, 2005, for example). Consider the change in total stored energy dU, and the change in (a single side of) crack surface area dA, associated with an infinitesimal increase da of the crack radius a. For the present case, the corresponding increment in crack surface area is: (1)


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Since the size of all regions scales with crack size, there is a transfer of material from region 1 to regions 0 and 2 whenever crack growth occurs. As a result of this transfer, the total stored energy U decreases by an amount dU, equal to the change in strain energy dU 1→0 of material transferred from region 1 to region 0, minus the change in strain energy dU1→2 of material transferred from region 1 to region 2. (2) Generally, the magnitude of the first term of Equation (2) is greater than the magnitude of the second, as crack growth tends to release stored energy. The terms in Equation (2) may be computed from the volume changes dV1→0 and dV1→2, and the average strain energy density of each region. The energy increment is now given by: (3) As argued previously, the average strain energy density in region 2 is higher than the remote strain energy density by a constant factor, i.e. W2=K1W1. Thus, the remote strain energy density may be factored out to obtain: (4) By virtue of axisymmetry, the volumes associated with the terms dV1→0 and dV1→2 are both proportional to a 2 da. Thus, a 2 da can be factored out, and the remaining constant terms may be collected into a single constant K2, giving:

(5) Thus, combining Equations (1) and (5), the energy release rate is:

(6) The value of K3 can be determined by assuming particular axisymmetric shapes for regions 0 and 2. Using a spherical shape for region 0, and neglecting region 2, K 3 works out to exactly 2. K3 may also be determined by comparing Equation (6) with solutions obtained independently of the present reasoning. From linear elastic fracture mechanics, the constant of proportionality for a penny shaped flaw is K3 = 8/π, or K3 ≈ 2.5. Although the arguments presented here were based on the particular case of an embedded penny-shaped crack, very similar arguments may be applied to small

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cracks of other geometries. Such exercises invariably yield a similar conclusion, that under remote uniaxial loading, the energy release rate is directly proportional to the far-field strain energy density, and the size of the crack. These arguments also illustrate why it is not consistent to regard that the factorisation T = C W a applies in cases of multiaxial loading, if C is assumed to be independent of mode of deformation. Specifically, in this case, region 0 cannot be fully relieved by the crack, rendering inapplicable Equation (3). Under multiaxial loading, a certain portion of the far-field strain energy density is not available to be released by virtue of crack growth, and therefore does not contribute to the energy release rate. 2.2 A HEURISTIC ESTIMATE OF ENERGY RELEASE RATE

In order to extend applicability of the factorisation T = C W a for cases involving multiaxial loading, it is desired to identify the portion of the total strain energy density W that is available to be released as the crack grows. A continuum mechanical parameter is now postulated which is intended to provide approximately such an identification. The parameter is called the cracking energy density, in order to distinguish it from the strain energy density, and in recognition of its purpose to approximate the energy release rate of a crack. This quantity is herein represented by the symbol Wc. In the context of elasticity, each plane at a given point is associated with a quantity of energy that is equal to the work performed by the tractions acting on the surface during the process of deforming the surface. It is postulated that this energy can be identified as available to be released by a crack in the given plane. The increment in cracking energy density dWc is given by the dot product of the traction vector with the corresponding strain vector increment . (7) Note that this definition accounts for both normal and shear loadings of the given → surface. The traction vector σ is defined for a given stress state σ, and a given material plane defined by a unit normal vector, . (8) The strain vector quantifies, for the given strain state ε, the normal and shear strains associated with a vector in the direction of the material plane unit normal . It is given by: (9) Substituting Equations (8) and (9) into Equation (7),

(10) or, (11)


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For comparison, the strain energy density is given by: (12) Equation (11) gives the basic definition of cracking energy density. For a given crack orientation , this expression may be integrated to determine the cracking energy density Wc as a function of the strain state. For perfectly elastic situations, the cracking energy density, like the strain energy density, depends on the strain state, and is independent of the strain history. While the strain state alone uniquely determines the value of the strain energy density, the cracking energy density depends additionally on the material plane of interest, as specified through the unit normal vector . It is postulated that the energy release rate T can be factored into the cracking energy density Wc, the flaw size a, and a constant of proportionality C, as in Equation (13). It is suggested that this factorisation provides an approximation which is applicable for multiaxial loading, and for arbitrary crack orientation. This postulate was motivated particularly by experiments (Mars, 2002) involving crack growth of small inclined cracks under far-field simple tension. It was noticed that the present definition of available energy density provided an excellent prediction of the effect of crack orientation on the initial crack growth rate. (13)

A strain energy density-like parameter defined on a critical plane was proposed previously by Glinka, Shen, & Plumtree (1995) for use in metals, and has certain similarities to cracking energy density. Their parameter was postulated to represent “…a fraction of the overall strain energy density contributed only by the stresses and strains on the critical plane.” Their parameter W* was specifically formulated for the case of plane stress, and is defined in terms of the stress component ranges ∆σ21 and ∆σ22, and the strain component ranges ∆γ21 and ∆ε22 on the plane of maximum shear. While conceptually similar to cracking energy density, their definition does not readily generalize to cases of finite straining. Their parameter also presumes that the critical plane is the plane of maximum shear. In contrast, the cracking energy density makes no assumption regarding the orientation of the critical plane. This plane can be identified as the plane experiencing the most severe history of cracking energy density.

3 SMALL STRAIN, LINEAR ELASTIC FORMULATION OF CED Before considering the general case of finite strains, it is instructive to further develop and explore the cracking energy density for small strains. This puts off the need to distinguish between original and deformed coordinates until after the basic calculations have been introduced. For the present purpose, it is convenient to work in principal coordinates. Therefore, the cracking plane normal vector needs to be transformed into the coordinate system formed

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by the principal directions of the strain tensor. If κ is the transformation from original κ . The increment in cracking energy coordinates to principal coordinates, we have density dWc, in terms of the normal vector in original coordinates , and the principal values σ′ of the stress tensor σ, and the principal values dε′ of the strain increment tensor dε is:

(14) Both the total strain energy density W and the cracking energy density W c are independent of the strain path for elastic materials. In the following derivation, linear elasticity is assumed. Perfect, nonlinear elasticity will be addressed subsequently. Because of strain path independence of elastic materials, the cracking energy density can be obtained by integrating from the unstrained state to the strain state of interest along any convenient strain path. Choosing a strain path such that the strain components remain proportional (principal directions do not rotate), and noting that the transformation κ and crack orientation remain constant during integration results in:

(15) The outermost matrix factors contain the terms describing the crack orientation, and the transformation from principal coordinates. The matrix ψ represented by the bracketed factor in Equation (15) contains terms describing the energy density contributed by each stress/strain-increment pair in principal coordinates. Note that the strain energy density is the sum of the diagonal terms of this matrix. Also note that each integral in ψ is evaluated along a radial path from 0 to the strain state of interest, and that all strain components vary linearly with the variable of integration. For an isotropic, linear elastic material, the principal stresses can be computed from the principal strains by Hooke’s law:

(16) Thus, the matrix ψ is given by:

(17)


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Typically, for a given strain state, it is necessary to evaluate Wc over many potential crack orientations. The ability to factor the cracking energy density into a part due to the elastic constitutive behavior, and a part due to the orientation of the principal directions with respect to the cracking plane can be used to advantage in implementing an analysis for small strain situations. This advantage arises because ψ needs to be evaluated only once for a given strain state, and because ψ has a closed form expression. Only the linear elastic constitutive model is given here because this factorisation cannot be made in the case of finite strains. The calculation of the cracking energy density at finite strains is discussed next.

4 FINITE STRAIN, NON-LINEAR ELASTIC FORMULATION OF CED The necessity of accounting for finite strains and nonlinear elasticity quite obviously arises when rubber is subjected to deformations of sufficient severity to cause failure by fatigue or fracture. In order to make such an accounting, it becomes necessary to distinguish between deformed and undeformed configurations, and between references made to points embedded in the material and references made to points fixed in space. Making these distinctions naturally gives rise to two different approaches to the description and mathematical formulation of physical principles. Herein, these approaches are called the material description and the spatial description. While the definition for cracking energy density is perhaps easiest to state in terms of a spatial description, a material description is often used in finite strain elasticity. The use of a material description is also helpful in defining the cracking energy density because it refers to a particular material plane, not a fixed plane in space. In this section, a material description of the cracking energy density is formulated which remains valid at finite strains, and for nonlinear elastic materials. The initial formulation given is strictly valid only when the normal component of the traction vector on the cracking plane is tensile. When the normal component is compressive, the occurrence of crack closure necessitates a modified approach. The required modifications are briefly described. A final topic covered in this section concerns prediction of the plane of crack initiation. 4.1 CRACKING ENERGY DENSITY

The increment in cracking energy density dWc in the spatial description is defined in terms of the traction vector and a normalized displacement vector on a given plane in the instantaneous, deformed configuration.

(18) The normal to the plane is defined by the unit vector . The traction vector is expressed in terms of the Cauchy stress tensor T as:

(19)

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The unit deformation rate vector is expressed in terms of the deformation rate tensor D as:

(20) Thus, Equation (18) may be written as:

(21) Using the following relationships,

(22)

(23) we can convert from the spatial description to the material description.

(24) or,

(25) ρ/ρ0 is the ratio of the deformed mass density to the undeformed mass density (i.e. the ratio ~ of undeformed volume to the deformed volume), F is the deformation gradient, S is the 2nd Piola-Kirchhoff stress tensor, and E is the Green-Lagrange strain tensor. We now express the unit vector in the current configuration r→ in terms of the → corresponding unit vector in the undeformed configuration R . This ensures that the material plane is properly convected with the material while integrating from the undeformed state to the deformed state.

(26) Substituting into (25), we get,

(27)


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(28)

Expanding

, we see that

(29)

Of course, , where C is the Green deformation tensor and E is the Green-Lagrange strain tensor, therefore

(30) This final expression gives the cracking energy density in terms of the stress and strain measures of the material description, and in terms of a unit vector in the undeformed configuration. It is interesting to note that a simple exchange of energetically conjugate stress and strain measures from the spatial to the material description does not preserve the meaning of the cracking energy density at finite strains. This is in contrast to the strain energy density, which can be expressed, in either the spatial or the material description, as the scalar product of energetically conjugate stress and strain tensors. It can be shown that the difference arises due to cracking energy density’s reference to a particular material plane. It can be seen, however, that for small strains, the denominator becomes equal to unity, and 2E+I approaches identity. The material and spatial descriptions are therefore indistinguishable at small strains, as required. 4.2 CRACK CLOSURE

The cracking energy density formulation given above applies when the combined stress / strain state serves to open the crack faces. An important exception to the formulation given in the preceding section arises when the crack faces support a compressive normal load. In this case, the elastic energy stored due to the compressive component of the traction vector is not available to be released by crack growth, and should therefore be excluded from the cracking energy density. The formulation given above makes no consideration of the sign of the normal component of the traction vector. Note also that in the presence of crack face friction, a portion of the shear component of the traction may also be unavailable for release by crack growth, and this is not accounted for in the formulation given above. The approach used by the author has been to compute separately the independent contributions to cracking energy density due to the normal and shear components of the stress and strain. When the normal crack face traction is compressive, the corresponding

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normal contribution to cracking energy density is set to zero, while any shear contribution is retained. No attempt to incorporate the effects of crack face friction has been made, because of the resulting path-dependence. This approach is at least considered conservative, since the energy density available for crack growth is overestimated when crack face friction is neglected. 4.3 CRACK ORIENTATION

For simple strain histories (fully relaxing, constant amplitude, no crack closure except at fully unloaded state), the plane of crack nucleation may be computed from the hypothesis that the critical plane is the one that maximizes the cracking energy density. For these histories, the plane that maximizes the peak cyclic cracking energy density will also maximize the amplitude of cracking energy density, and will minimize the predicted fatigue life. It has been proved that, in many cases, the crack orientation that maximizes the cracking energy density is normal to the direction of maximum principal strain (and stress) (Mars 2001). For other, more complex strain histories, an algorithm is required to evaluate all possible planes, and to select those that result in the shortest computed fatigue life. The derivation given in (Mars, 2001) is based upon Equation (11), which is only valid in the absence of crack closure, i.e. when the normal component of the load on the cracking plane is tensile. When the cracking plane experiences compressive normal loading, the work done by normal components of the load should be disregarded, as discussed previously. In this case, planes other than the direction of maximum principal strain may be favoured for crack nucleation and growth – shear planes for example. In simple compression, planes normal to the direction of maximum principal strain are stress-free (Figure 3). Cracks in the plane

Fig. 3 Effect of simple compression on planes of various orientations.


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transverse to the compression direction experience closure. The planes which maximize the cracking energy density (with closure effects) in this case are shear planes which experience combined mode II shear and mode I compression.

5 THEORETICAL INVESTIGATIONS OF MULTIAXIAL EFFECTS Several aspects of the multiaxial behaviour predicted by cracking energy density have been investigated. The effect of biaxiality on the ratio of the cracking energy density Wc to the strain energy density W is first presented for the case where the cracking plane is fixed. Next, the effect of cracking plane orientation on the ratio Wc/W, for several levels of biaxiality is presented and compared with the corresponding results from linear elastic fracture mechanics. 5.1 EFFECT OF BIAXIALITY RATIO

Biaxiality was quantified as the exponent B in the following relationship between the first principal stretch λ1 and the transverse stretch λ2. (31) Thus, B may be computed as

(32)

Note that it is only necessary to consider B < 1, since for B > 1 a 90° rotation of the coordinate system yields an equivalent state with B < 1. Using the incompressibility constraint, 1 = λ1λ2λ3, the out-of-plane stretch λ3 can also be computed. (33) This definition of stretch biaxiality has the advantage that commonly investigated stretch states can be represented by a constant value of B over the entire range of λ1. For example, a simple tension test always corresponds to B = -0.5, even at finite strains. Values of B for stretch states commonly encountered in laboratory specimens are given in (Mars, 2001). Note also that for small strains, B is the ratio of the axial and transverse engineering strains, since . We now apply the linear elastic definition of cracking energy density given in Equation (15). For the present case, κ = I and . Additionally, for small strains,

(34)

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From Hooke’s law, and the plane stress condition σ3 = 0, (35) From these relationships, it can be shown that

(36) recalling that, W = tr(

), we have

(37)

(38) The small-strain incompressibility condition is given by v = 0.5. Figure 4 shows how the ratio of the cracking energy density to the strain energy density Wc/W varies as a function of stretch biaxiality B, when the cracking plane is held constant in an orientation transverse to the 1 direction. It can be seen that for simple tension, the ratio Wc/W is unity. This is consistent with the claim that the energy release rate can be factored into the strain energy density and the crack size a, for uniaxial tension, i.e. T ∝ Wa. Another commonly encountered strain state, planar tension, also has Wc/W = 1. For pure inplane shear, Wc/W = 0.5, and for equibiaxial tension Wc/W = 0.5. An interesting feature of the relationship between Wc/W and B is the maximum reached between the values of B = -0.5 and B = 0. For the linear elastic, small strain case, at a value of B = -0.262, (Wc/W)max = 1.074. Apparently, over a small range of biaxiality, the cracking energy density is somewhat greater than the far-field strain energy density. Closer examination of this case reveals that the surplus energy is provided at the expense of the transverse plane, for which a negative cracking energy density is computed. It appears that Poisson coupling of the axial and transverse stresses gives rise to this result. It will be shown subsequently that such an effect (i.e. available energy density greater than the strain energy density) is consistent qualitatively with the predictions of Linear Elastic Fracture Mechanics. 5.2 EFFECT OF CRACK PLANE ORIENTATION

In this exercise, the effect of crack orientation on the ratio W c/W, for the case of plane stress, has been investigated. The crack orientation θ is illustrated in Figure 5, which also shows how the ratio W c/W varies with crack orientation θ , for various values of B. In all cases, the ratio is maximized when the crack normal is aligned in


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Fig. 4 Effect of biaxiality B on ratio of cracking energy density to strain energy density. (1: also known as “simple shear”. 2: also known as “pure shear”.)

the direction of maximum tensile strain. Note, however, that the variation with θ decreases as B → 1. This reflects the fact that in equibiaxial tension, the crack can initiate at any orientation in the plane. It can be shown that the dependence on crack orientation given in Equation (38) is exactly equivalent to the solution from linear elastic fracture mechanics (LEFM), for the case of simple tension, B = -0.5. For arbitrary strain state, the solution from LEFM is given by

(39)

(40) where β is the stress biaxiality ratio, β = σ2/σ1, σ1>σ2 . It can be shown, from Hooke’s law, that

(41)

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1.2

l1

1 q

l2 = lB1

0.8 0.6 Wc W

B = + 1.00 B = + 0.625

0.4

B = + 0.25 0.2 B = – 0.50 0 B = – 0.25 – 0.2 0

15 30 45 60 75 Crack Orientation Angle q, degrees

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Fig. 5 Effect of crack orientation θ on ratio of cracking energy density to strain energy density.

The energy release rate T is computed as (42) which after some manipulation yields,

(43)

The ratio

can be evaluated for constant W by recalling that . Thus,

(44)


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If the energy release rate can be factored with cracking energy density as T = C Wc a, it should also be true, by comparison of Equation (43) with Equation (38), that

(45)

Plots of Equations (44) and (45) are shown in Figure 6. While the two relationships show similar trends with B, they are not identical. In some cases, they are different by as much as a factor of two (at B = 1). Thus, the cracking energy density Wc can at best be regarded as an approximation of the energy release rate. Note in Figure 6 that the available energy density predicted by linear elastic fracture mechanics (LEFM) can be greater than the far-field strain energy density, by as much as 30%. Momentarily ignoring the differences implied by Equations (44) and (45), full equivalence of Equations (43) and (38) additionally would require that

(46)

Fig. 6 Comparison of cracking energy density with Linear Elastic Fracture Mechanics. Wc/W is given by Equation (45) (cracking energy density). T(B,0°)/T(-0.5,0°) is given by Equation (44) (LEFM).

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A comparison of the right and left hand sides of Equation (46) is shown in Figure 7. It is again observed that the relationships are not identical, but that they do exhibit similar dependence on B. It is thus concluded that the dependence of the cracking energy density on both B and θ resembles, imperfectly, that of the energy release rate, over a considerable range, as shown in Figure 8. The agreement is particularly good as the crack orientation becomes transverse 10 9

β2 LEFM

8 7

f(B)

6 5 4 3 2 CED 1

B (B + v)(2v – 1) 2Bv2 + (2 – B)v – 1

0 –1 –2

–1.5

–1

–0.5 0 Biaxiality, B

0.5

1

Fig. 7 Comparison of cracking energy density with linear elastic fracture mechanics (LEFM). The parameter associated with cracking energy density is defined by Equation (46). The parameter β associated with LEFM is given by Equation (41).

Fig. 8 Comparison of cracking energy density (left) and linear elastic fracture mechanics (right) over a wide range of biaxiality and crack orientation angle.


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to the load (since as θ → 0, sin2θ → 0), and for B < -0.5. Agreement is exact for the case of simple tension, for all θ. Agreement is worst for B = 1, pure equibiaxial tension loading. In that case, LEFM predicts that the available energy density is equal to the strain energy density. Cracking energy density predicts that the available energy density is 1/2 of the far-field strain energy density, at both small and large strains. Yeoh (2002) has analyzed cracks under several modes of deformation via finite element analysis. His analysis gives strain energy release rates for the cases of simple tension TST = T(B = -0.5), planar tension TPT = T(B = 0), and equibiaxial tension TEB = T(B = 1). Further study of these results shows that for I1-3 > 2 (in simple tension ε > 100%, in equibiaxial tension ε > 50%), the ratio of the energy release rate TEB / TST ≈0.6, when compared at equal strain energy density (as estimated via I1-3). I1-3 is proportional to strain energy density for the neo-Hookean model that was used. Thus, this result is in rough agreement with the prediction of cracking energy density that TEB / TST ≈ 0.5. For smaller strains, Yeoh found that TEB / TST → 1, in agreement with LEFM. It is also noted that several investigators (Roberts and Benzies, 1977; Roach, 1982) have obtained experimental fatigue crack growth results implying that the available energy density in equibiaxial tension is roughly 1/2 of the far-field strain energy density. It thus appears that at finite strains, cracking energy density falls within the range of estimates made in previous reports, and therefore provides a usable first approximation of the dependence of energy release rate on mode of deformation.

6 CONCLUSIONS A heuristic theory for estimating the energy release rate of a small crack of arbitrary orientation and remote loading has been presented. The theory attempts to address several factors considered important for highly deformable, elastic materials. Specifically, these are 1) finite strains, 2) nonlinear elastic constitutive behaviour, and 3) crack closure. Comparison of the theory with linear elastic fracture mechanics shows similarity over a large range of crack orientation and stretch biaxiality. Differences in the predictions of the respective theories have been identified and discussed. Since the cracking energy density is evaluated at a material point in the uncracked material, this parameter can be particularly useful for the analysis of crack nucleation from initially unobserved flaws.

ACKNOWLEDGEMENTS This investigation was conducted as part of the author’s doctoral dissertation, completed at the University of Toledo in 2001. The authors academic adviser, Dr Ali Fatemi, is gratefully acknowledged. Funding for this work was provided by the Cooper Tire & Rubber Company.

SYMBOLS a, A,

characteristic crack length (radius) crack surface area

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B, β, C, C,

stretch biaxiality ratio stress biaxiality ratio constant of proportionality Green deformation tensor (also known as the right Cauchy-Green deformation tensor) d, characteristic length of region over which crack tip energy density is averaged →, D deformation rate vector associated with a particular material plane of interest D, deformation rate tensor E, Green-Lagrange strain tensor. dε→, strain vector increment associated with a particular material plane of interest ε, small strain tensor ? = denotes a hypothetical equality which is to be tested F, deformation gradient G, shear modulus or strain energy release rate KI, KII mode I and mode II stress intensity factors κ, transformation matrix from original to principal coordinates λ1, λ2, λ3, first, second, and third principal stretches ν, Poisson’s ratio r→, unit vector in the deformed configuration, defining material plane of interest. → R, unit vector in the undeformed configuration, defining material plane of interest. ρ/ρ0, ratio of the deformed mass density to the undeformed mass density (i.e. the ratio of undeformed volume to the deformed volume), ~ 2nd Piola-Kirchhoff stress tensor S, → σ, traction vector σ, T, Cauchy stress tensor → T, Cauchy traction vector associated with a particular material plane of interest T, strain energy release rate (sometimes written as G) θ, Crack orientation K1, K2, K3, constants of proportionality W, strain energy density Wc, cracking energy density W1, W2, strain energy density of regions 1 and 2 U, total stored strain energy Ψ, matrix containing terms describing the energy density contributed by each stress/strain-increment pair in principal coordinates

REFERENCES Azura AR & Thomas AG (2005) “Effects of heat ageing on crosslinking, scission and mechanical properties” (This Volume). Chang YW, Gent AN & Padovan J (1993) “Strain energy release rates for internal cracks in rubber blocks”, Int J Fracture, 60, 363-371. Glinka G, Shen G & Plumtree A (1995) “A multiaxial fatigue strain energy density parameter related to the critical fracture plane”, Fatigue and Fracture of Eng Mat and Struct, 18, 37-46.


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Lake GJ & Thomas AG (1998) “Strength properties of rubber” Chapter 15 in Natural Rubber Science and Technology, AD Roberts (ed) Oxford, 731-772. Mars WV (2001) “Multiaxial fatigue crack initiation in rubber”, Tire Science and Technology, 29, 171-185. Mars WV (2002) “Cracking energy density as a predictor of fatigue life under multiaxial conditions”, Rubber Chem Technol, 75, 1-17. Mars WV & Fatemi A (2001) “Criteria for fatigue crack nucleation in rubber under multiaxial loading”, Constitutive Models for Rubber II, Besdo, Schuster & Ihlemann (eds), Swets & Zeitlinger, The Netherlands, 213-219. Mars WV & Fatemi A, (2002) “A literature survey on fatigue analysis approaches for rubber”, Int J Fatigue, 24, 949-961. Roach JF (1982) “Crack growth in elastomers under biaxial stresses”, PhD Dissertation, University of Akron. Roberts BJ & Benzies JB (1977) “The relationship between uniaxial and equibiaxial fatigue in gum and carbon black filled vulcanizates”, Proceedings of Rubbercon ’77, 2.1, 2.1-2.13. Yeoh OH (2002) “Relation between crack surface displacements and strain energy release rate in thin rubber sheets”, Mechanics of Materials, 34, 459-474.

CHAPTER 8

Abrasive Wear of Elastomers VA Coveney and DE Johnson University of the West of England, Bristol, UK

SYNOPSIS Many elastomer products come to the end of their useful life through abrasive wear (wear brought about through local or general sliding); however the processes of abrasive wear are complex and challenging. Approaches towards improved understanding and prediction of abrasive wear under various conditions are outlined. The most fully developed class of model is that originated by Southern & Thomas (1978) who consider abrasion under conditions of moderate-to-high tangential contact stress; they envisage abrasion progressing by fatigue crack growth at the roots of macroscopic flaps or “tongues” of rubber. The Southern & Thomas model fits some experimental observations but not others. The roles of temperature, oxygen and mechano-chemical effects are discussed (Gent & Pulford, 1983). Experiments are described in which five materials [based on natural rubber (NR), acrylonitrile butadiene (NBR) and ethylenepropylenediene (EPDM)] were abraded with a (blunt) “blade”. Evolving visual patterns and patterns of blade abrader force were monitored as was material loss. Similarities between the visual wavy (Schallamach) patterns, often associated with rapid wear, and the force patterns suggest a close relationship between the two. The fact that force patterns, of a wavelength which persists, are discernable from the start of scraping suggests that aspects of the Schallamach pattern have their origin in non-destructive abraderelastomer interactions. For unidirectional abrasion the wear rates observed under similar conditions and for elastomeric materials of similar hardness varied widely – NR at 55 International Rubber Hardness Degress (IRHD) giving 60 times the wear rate of 55 IRHD EPDM – for which no Schallamach pattern was observed. In bidirectional abrasion, wear rates were generally a little lower than under unidirectional conditions but the reduction was rather minor. Although there has been considerable progress made, a comprehensive quantitative theory of abrasion of rubbery materials is still to be developed.

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Elastomers and Components: Service Life Prediction – Progress and Challenges 1 INTRODUCTION

1.1 DEFINITIONS, ECONOMIC ISSUES

Abrasive wear of rubber can occur whenever there is general sliding, as in a sliding seal for example, or local sliding as at the edge of the contact patch of a rolling tyre. The subject is of enormous economic and environmental importance. For example, in the UK alone in the region of 5×104 tonnes of tyre wear debris are generated and 5×107 tyres are scrapped every year. Failure by abrasion of a low cost seal can have major cost or safety implications. However, the study and analysis of abrasive wear of elastomer components still poses many challenges despite 50 years of study – because of the complexities of deformation and sliding and because of complexities in material removal mechanisms themselves (Muhr & Roberts, 1988). There are also differences in terminology. For some, abrasion refers to surface damage and material loss when only when the sliding is well defined. For others, abrasion refers only to very sharp and/or well-lubricated abraders and /or relatively high modulus rubbery or other polymeric materials. In this chapter, “abrasion” and “abrasive wear” will have a general meaning. Abrasive wear can include 3body situations (Coveney & Menger, 2000) as well as 2-body cases (as in abrasion by asperites). Other related phenomena include erosion of elastomers caused by impacting particles (Arnold & Hutchings, 1992; Arnold, 1997). Standard methods of abrasion testing of elastomer testpieces include the Akron and the DIN abrasion tests (BSI, 1987; ISO, 1985). The Pico blade abrader test is also sometimes used (Newton et al, 1961). However, such standard methods often do not correlate with in-service abrasive wear. Moreover there is no overall quantitative, predictive understanding of abrasion of rubbery materials, therefore costly timeconsuming component testing is widespread. 1.2 TYPES OF ABRASION

The type of abrasive wear occurring at an elastomer surface depends on the material, the prevailing conditions and the history. A significant complicating factor is the influence of the rubbing on the harder surface. Deposition of contaminant material, polishing and free radical chemistry can all play a part (Veith, 1986; Gent & Pulford, 1978; Coveney & Menger, 2000). When normal stresses are high (~100 MPa) but frictional stresses are not, scoring of the elastomer (grooves in the direction of sliding) may dominate – as frequently observed in harder polymers. When surface stresses are low (~0.1 MPa or less at the macroscopic scale) “intrinsic” (i.e. patternless) abrasion may often occur – manifested as “smearing” and/or roll formation (production and removal of a high viscosity or plastic layer at the surface) or as non-smearing (microscopic) particulate debris (Medalia, 1994; Grosch, 1996; Veith, 1986). Smith & Veith (1982) and Veith (1986) point out that tyre debris is generally composed of degraded tread material and road debris (“silt”) and that such material also comprises a ~1µm layer on the worn tread surface; they argue that tyre abrasion is thus actually 3-body abrasion (road surface, undegraded tread and a mixture of degraded rubber and “silt”). Gent & Pulford (1983, 1-5µm) and Gerrard & Padovan (2002, 1-10µm) assert that in non-smearing (or particulate) intrinsic abrasion the diameters of the debris particles are predominantly in the µm range. When frictional stresses are moderate-to-high in unidirectional sliding a characteristic

Abrasive Wear of Elastomers

115

wavy surface pattern is often in evidence; this is known as the Schallamach (abrasion) pattern (Figures 1 and 2); the ridges run perpendicular to the direction of sliding. As abrasion progresses, the Schallamach pattern drifts in the direction of the abrader sliding. Schallamach pattern abrasion is often associated with high rates of material loss (Muhr & Roberts 1988, 1992). The majority of published laboratory studies of abrasive wear of elastomers have focused on unidirectional sliding under steady conditions. The reasons are clear enough: even highly simplified situations of abrasion – such as unidirectional sliding by a blade abrader under nominally constant loading or constant indentation conditions – are complex. Also, unidirectional sliding (especially over a long distance) has the advantage that the sliding distance is accurately known despite the compliance of the elastomer. It needs to be borne in mind, however, that steady conditions can take a significant amount of time to develop (Coveney & Menger, 1999; Menger, 2001). Schallamach (1958) states that if the direction of sliding is regularly changed (by 90°) the Schallamach pattern is not observed, instead “intrinsic” abrasion occurs and abrasion loss is reduced – by a factor of 2 approximately. 1.3 ATTEMPTS TO UNDERSTAND AND MODEL ABRASIVE WEAR

Attempts at understanding abrasive wear should start with the basic aspects of the interaction between the rubbery material and the more rigid counterface – including their initial geometries and the deformations and stresses resulting from their interaction. In the case of tyre wear for example, the macro and the micro texture of the road surface have usually been referred to (Veith in Pottinger, 1986; Gerrard & Padovan, 2002). However it has been suggested recently that many surfaces, road surfaces among them, are well described by (self-affine) fractal texture models with upper and lower cut-off length scales (Heinrich, 1997; Persson & Tossati, 2000; Kluppel & Heinrich 2000). The lower cut-off length will depend on whether the surface is wet or dry, the degree of contamination of the surface and the degree to which the aggregates are polished (Persson & Tossati, 2000; Persson, 2004). The lower cut-off length may be surprisingly small but can be assumed to be above the nm scale. This view leads to the interesting conclusion that while the normal stress acting between a tyre tread and the road surface is ~0.3 MPa at the cm scale it may be rather large (~30MPa) at the µm scale (Westermann, 2004). Muhr & Roberts (1988, 1992) have discussed adhesion between a rubbery material and a more rigid counterface. However, it can be argued (Persson, 2000 and Mori et al, 1993 & 1994) – that for practical rubber materials, for sliding rates ~10 mms-1 at around room temperature, if the average normal stresses are above ~0.02 MPa (at the ~mm scale) then adhesive forces are insignificant compared to externally applied loads; also, the externally applied loads are believed to keep the rubber and the surface in intimate contact down to (sub)microscopic scales during (clean, dry) sliding. Thus the surface layers of rubber are subjected to stress histories with characteristics related to: sliding speed; surface profile of the counterface; the length of the contact patch over which sliding occurs (which depends on a number of factors); the time, temperature and strain dependent viscoelastic “moduli” of the rubber (see Persson, 2000, for example). [Wet sliding introduces further complications as discussed by Menger (2001) and Persson (2000).] The depth to which the main contact-related stresses are developed in the rubber material will be of the same order as the roughness scale considered. (The overall effect is

116


Fig. 1 Images (of 7.5 x 5.5mm areas of elastomer surface) showing development of pattern between 100 and 1000 cycles of unidirectional abrasion [30N load, 27mm/s velocity, effective sliding direction of blade from left to right].


117

NR45

NR55

NR65

NBR

EPDM

0

10 mm

Fig. 2 Cross-sections of unidirectional abrasion test pieces after 1000 cycles. [Effective sliding direction of blade from right to left.]

the combination of effects at many different length scales.) It is now believed that the bulk (but near-surface) response to the roughness-generated deformation history is the origin of stick-slip friction in most cases (Heinrich, 1997; Persson, 2000; Kluppel & Heinrich 2000). Because of the large stresses and short time-scales (high frequencies) associated with rubber deformation caused by sliding over microscopic and sub-microscopic asperities, there can be high local rates of viscoelastic energy dissipation (Daley, 2005; Grosch, 1996). Local heating will occur as a consequence of the energy dissipation (“friction”) effects just described, together with any other heat generating effects present. As temperature rises, the dissipative component of force and, so, the frictional force decreases so that in due course cooling can occur – leading, potentially, to history dependent stick-slip behaviour (Persson, 2004). Such an account is in contrast to the “traditional” attempted explanation of stick-slip in terms of a velocity-dependent friction coefficient (Rorrer, 2000). Muhr & Roberts (1992) review initiation of (non-smearing) abrasion. Gent (1989) suggests that triaxial tensions on pre-existing microscopic voids may have a role in the initiation of abrasive wear. Fukahori & Yamazaki (1994a, 1994b & 1995) have proposed that strong (~1g) microvibration of the rubber surface (at ~500Hz-3 kHz) causes impacts with, and thus adhesion to, the asperity followed by fracture and detachment of rubber. Fukahori & Yamazaki found that the microvibration frequency agreed “with the intrinsic natural frequency of rubber, separately measured by the natural drop of the weight on the surface of the rubber

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Dy

Blade z Fx

Tongue/flap x

q

y

Crack

Fig. 3 Blade abrader and idealised flaps.

specimen.” They also observed initiation cracks which they believed to be spaced according to the frequency of the microvibration. Fukahori & Yamazaki maintained that the microvibration-related spacing gradually increased to give the larger scale Schallamach pattern. (See also Furukawa, 1996.) Coveney & Menger (1999) – using a very stiff apparatus – were unable to detect initial microvibration of the type and frequency described by Fukahori & Yamazaki (1994a, 1994b) while using an otherwise similar blade abrader arrangement. Some local high frequency lower amplitude oscillation may very well occur nevertheless. Coveney & Menger (1999) did observe lower frequency (~10Hz) force oscillations believed to be associated with gross stick-slip behaviour. Persson & Tosatti (2000) have put forward arguments to relate high rates of abrasion wear, in skidding for example, to conditions in which small scale (hard) surface roughness produces strains in the elastomer of such high frequency that particles of elastomer break away by brittle fracture. [They also point to the possible role of brittle (aged) surface layers in abrasion of elastomers.] There is general agreement that abrasion loss depends strongly on the frictional work. It has been variously proposed (Grosch, 1996) that surface damage leading to wear may occur as a result of: (i) (often oxidative) ageing accelerated by the high temperatures produced wholly or partially as a result of sliding friction; (ii) stress-induced polymer chain scission; (iii) crack propagation rate as a function of the strain energy release “rate” T. [In a strained piece of rubber, formation of unit area of crack releases strain energy, T, previously stored. The concept put forward by Rivlin, Thomas and others is that T drives the crack growth (Rivlin & Thomas, 1953; Azura & Thomas, 2005).] Southern & Thomas (1978) put forward a model for Schallamach pattern abrasion under steady abrasion conditions. They envisaged crack propagation by frictional pulling (by a blade or other asperity) of flaps, or “tongues”, of rubber (Figure 3). Comparing the situation with that of the standard tear testpiece Southern & Thomas (1978) proposed

(1)


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Here Fx is the horizontal abrading force exerted; ∆y is the width of the rubber testpiece or blade (whichever is narrower); θ is the “dive” angle of the abrasion pattern as it drifts as the surface wears away – that is the angle the notional crack makes with the direction of abrader sliding along the undamaged surface (x). Southern & Thomas (1978) estimated θ from the lateral shift of the abrasion pattern per blade abrader pass

(2) and from the mass of material lost per pass

(3)

[Here n is the number of blade abrader passes; the total rate of movement (per pass) of the pattern the notional crack growth rate; ∆x is the horizontal distance travelled by the abrader along the rubber surface per pass; ρ is the density of the rubber.] Therefore

(4)

and

(5) For a variety of unfilled rubber materials Southern & Thomas (1978) plotted, on loglog scales, notional crack propagation per pass ∂c/∂n [see Equation (5)] against notional strain energy release rate T [see Equation (1)] for abrasion and compared these points with data from fatigue tests (Figure 4). The abrasion was performed on the outer surface of a 12.5mm wide, 63.5mm diameter disc rotating at 34.1 mm/s (Southern & Thomas, 1978 and Muhr, Pond & Thomas, 1987). The fatigue data were from experiments at unstated (but presumably low, i.e. ~1Hz) frequencies on edge cracks in simple extension testpieces (Lake & Lindley, 1964). Good agreement was obtained between abrasion and fatigue results for styrene butadiene rubber (SBR); quite good agreement was obtained for acrylonitrile butadiene rubber (NBR) and for isomerised natural rubber (NR); for butadiene rubber (BR) the agreement was fair. In contrast, for normal NR the abrasion loss very greatly exceeded predictions based on crack growth data – indeed the abrasion loss resembled, but was systematically lower than, the loss for isomerised NR; for highly crosslinked NR agreement was better – although the crack growth predictions significantly exceeded the abrasion loss.

120


100 NBR * NBR* 10

BR *

dc/dn

∂c/∂n

BR* SBR *

1

SBR* NR (isomerized)* NR (isomerized)*

0.1

NR65 NR55 0.01

NBR 0.1

1

10

T Fig. 4a Comparison of abrasion results (points) and fatigue crack growth results (lines) from Southern & Thomas* (1979) with current experimental results. (Notional tearing energy T = Fx /∆y (1 + cosθ) [kN/m], notional crack growth rate ∂c/∂n = (∂m/∂n)/(∆x∆y ρsin θ)[µm/cycle]).

100 Highly crosslinked * Highly crosslinked* Isomerized *

10 ∂c/∂n

dc/dn

Isomerized* NR * NR*

1

NR45 NR55 NR65

0.1 0.1

1 T

10

Fig. 4b Comparison of NR abrasion results (points) and fatigue crack growth results (lines) from Southern & Thomas* (1979) with current experimental results. (Notional tearing energy T = Fx / ∆y(1 + cosθ) [kN/m], notional crack growth rate ∂c/∂n = (∂m/∂n)/(∆x∆y ρsin θ) [µm/cycle]).

The high extensibility and strength properties of normally cross-linked NR, achieved with little or no filler, is often associated with the tendency of NR to crystallise at large strains. Of the elastomers tested, isomerised NR, BR, SBR and NBR were classed as non strain-crystallising, NR as strain-crystallising and highly crosslinked NR as less readily crystallising.


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Southern & Thomas (1978) stated that changing the sliding velocity by a factor of two in their abrasion experiments made no appreciable difference to abrasion loss per pass etc. They found that the notional dive angle (θ ) was small (typically 1-15°). They commented that ridge spacing in the Schallamach pattern appeared to be approximately proportional to the horizontal abrading force Fx . They also commented on how the pattern differed, and changed differently with temperature, for different elastomers. They asserted that there was little pattern if the test temperature was within 50°C of the glass transition temperature, while there was a fine pattern if the temperature was more than about 130°C above the glass transition. Muhr et al (1987) noted that the Southern & Thomas model overpredicted abrasion losses for lubricated conditions; they suggested that under such (low friction) conditions the flaps may not flip as in Figure 3 but may be compressed instead. They gave the following equation for strain energy release rate for abrasion where the flaps are merely compressed.

(6) Here E is the Young’s modulus, d is the flap thickness and Λ is the extension ratio of the flap. Muhr et al (1987) state that Equation (6) often gives lower values of T than does Equation (1). Lower values of T would give rise to lower rates of crack growth and so lower abrasion loss. However it is also clear that in unlubricated circumstances the role of θ is crucial – but the reason for a particular value of θ occurring has yet to be explained. Medalia et al (1992) and Stupak et al (1988,1990) point to the extremely complex details when Schallamach abrasion patterns are examined closely. Indeed, Medalia et al (1992, page 173) question whether (apparent) flaps really are flaps in practice and prefer to call these ridge-like features “shingles”. Applying Persson & Tosatti’s (2000 and see above) line of argument to the Southern & Thomas (1978) experiments indicates that sub-nanometre roughness length scales (~0.1nm or less) would be required for glassy behaviour. Glassy behaviour thus appears unlikely in these experiments – a conclusion supported by the generally reasonable-to-good agreement between abrasion and low frequency fatigue behaviour found by Southern and Thomas (1978). Adopting a strain energy release rate approach, Gerrard & Padovan (2002, 2003) ascribe a central role to 1-10µm diameter rubber nodules, and their fatigue, in all types of (nonsmearing) abrasion and put forward an outline conceptual framework for history-dependent effects observed when the abrasion direction is changed. Gerrard & Padovan (2002, 2003) do not, however, account for the association between Schallamach patterns and high abrasion rates (see Southern & Thomas, 1978 and below). Gerrard & Padovan’s conceptual framework remains to be fully developed and tested. Dannenberg (1986) states that in tyre abrasion, local temperatures are likely to reach 240°C and cites Grosch as proposing that “all severity effects are really disguised temperature effects if temperature is measured at the tread surface.” Williams & Cadle (1978) and others have found evidence of elastomer degradation during abrasion; Dannenberg (1986) associated the degradation and the hydrocarbons emitted during abrasion with the involvement of localised high temperatures. Williams & Cadle themselves draw an analogy with “mastication” (during rubber processing to reduce molecular weight).

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Gent & Pulford (1983) performing blade abrader experiments for moderately low wear rates (generally ~100nm or less per pass), found that smearing and non-smearing abrasion of SBR was typically twice as fast at 100° C as at 25° C – rather than orders of magnitude faster as for fatigue crack growth. Gent & Pulford also reported that in air, unfilled NR, SBR and BR and filled (approximately 50 parts of N330 carbon black per hundred by weight of polymer) BR and trans-polypentenamer gave non-smearing (particulate) abrasion. In air for filled NR and SBR abrasion was smearing in type – as it was for filled NR in the absence of air but in the presence of the free radical acceptor thiophenol. For filled NR and SBR in the absence of air or thiophenol, abrasion was non-smearing. In air or in its absence, filled ethylene propylene diene rubber (EPDM) gave smearing abrasion. Gent & Pulford also found that the abrasion rate was proportional to a lower power of the tangential force (hence frictional work done) for filled (1.5-1.8) than for unfilled materials (2.5-3.5). Gent & Pulford’s work indicates that chain scission caused by oxidative attack is not the sole cause of smearing abrasion. Gent & Pulford interpreted their observations as evidence of the dominant role played by mechano-chemical degradation (i.e. mechanical stresses causing scission of the polymer chains and resulting free radicals reacting with oxygen or other substances present) in abrasion – as opposed to temperature-driven oxidative processes. Like Williams & Cadle (1978), Gent & Pulford (1983) draw an analogy with “cold mastication” (Bristow & Watson, 1963; Brydson, 1978). The evidence put forward by Gent & Pulford makes it seem likely that mechano-chemical degradation does indeed play a role, some counter-indications notwithstanding (Muhr & Roberts, 1988; Jacobson, 1999). However it is difficult to believe that little or no part is played in tyre abrasion, for example, by the very high very local transient temperatures for which there are considerable theoretical and experimental indications – as argued by Persson (2004) and above. Thus it is possible that Gent & Pulford’s experiments were not sufficiently representative of tyre tread wear conditions. Alternatively it may be possible that as the temperature of the polymer rises, the rate of heat generation correspondingly decreases very significantly so that the effect of a higher environmental (starting) temperature is lessened (q.v. above: discussion of stick-slip behaviour by Persson). Gent & Pulford (1983) and also Veith (1986) see elastomer abrasion as a competition between mechano-chemical degradation processes and fracture processes (q.v. (ii) and (iii) above). To summarise progress towards understanding and modelling abrasion. Although there is striking agreement between low frequency, room temperature fatigue crack growth data and abrasion data via the Southern & Thomas (1978) model in some cases, in other cases the agreement is poor. [Various suggestions have been made on why the Southern & Thomas model sometimes fails and how the model might be improved: Muhr & Roberts, 1988 (prevention of strain-crystallisation by high temperatures); Muhr et al, 1987 (buckling mode of crack propagation); Brydson,1978 (prevention of strain-crystallisation by oxidation).] Also, the Southern and Thomas class of models: fail to describe how the cracks are initiated; seem at odds with some aspects of the details of the development and the visual appearance of pattern abrasion; are not applicable to the patternless abrasion observed at lower wear rates, for example on the treads of radial tyres. At low wear rates mechano-chemical effects appear to play a key role (Gent & Pulford,1983) – although it seems likely that high temperatures often have a significant influence. As Veith (1986) points out, wear is a complex physical-chemical process. The importance of “competing processes” in abrasion appears to be widely accepted – although questions remain on details of the competing processes. Quantitative “multiphysics” modelling is required to embrace the complexity and to facilitate thorough


123

examination of outline models for abrasion and the boundaries between the competing processes to be predicted. A number of authors reporting research – and one of the standard laboratory test methods – use a blade abrader. Such arrangements have both the advantages and disadvantages of simplicity. We have performed experiments using a highly instrumented and adaptable blade abrader apparatus in order to examine in more detail some aspects of rubber abrasion under high tangential stress conditions.

2 EXPERIMENTAL MATERIALS, APPARATUS AND METHOD 2.1 MATERIALS

Experiments were performed on five elastomeric materials; three had natural rubber (NR) as the base polymer, one acrylonitrile butadiene rubber (NBR) and the fifth, ethylene propylene diene rubber (EPDM). The elastomer formulations are shown in Table 1. Three of the vulcanised materials had similar nominal IRHD (international rubber hardness) values: 55 IRHD. All the materials tested were filled with carbon black. However the 45 IRHD NR material (NR45) was only lightly filled with a carbon black unlikely to greatly affect material properties. The elastomer testpieces were rectangular blocks 200 x 100 x 20mm (length x breadth x thickness) bonded during vulcanisation to steel plates (260 x 100 x 4mm). 2.2 DESCRIPTION OF APPARATUS

The experimental apparatus shown in Figure 5 was previously described by Coveney & Menger (1999). An elastomer testpiece is attached to a small-scale linear slip table driven by a servohydraulic ram. A “single sided” “blade abrader” was used in for the unidirectional tests and a “double sided” blade for the bi-directional tests (Figure 5b). The abrader was attached to a 6-degree-of-freedom force/torque transducer and a digital camera with a lighting ring to give high contrast. A PC was used to acquire force and displacement data during each abrasion “pass”, using custom-written software . The same PC also controlled the slip table and a stepper motor which, for unidirectional tests, lifted and lowered the blade at the end and beginning of each abrasion pass respectively. Moreover the control computer controlled a second PC which ran a frame capture program. In measurements and observations of abraded surfaces the following instruments were used: vernier callipers for overall depth checks; a small depth-of-field microscope fitted with a dial gauge for local depth measurement; a large depth-of -field stereo microscope for assessment of topography and form. 2.3 EXPERIMENTAL METHOD

All experiments were performed in a temperature controlled room at 23 ± 3 °C. Testpieces were conditioned at this temperature for at least 24 hours prior to testing. For unidirectional tests the applied displacement waveform was a modified sawtooth. The abrasion stroke of 90mm was at a constant rate (27 mm/s), the return stroke approximately 50mm/s with initial acceleration and final deceleration periods (to avoid shock induced

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Table 1 Formulation of rubber testpieces in parts per hundred of rubber (by weight). (IRHD: International rubber hardness degrees. Natural rubber: Standard Malaysian Rubber, SMR CV 60.)

vibration of the apparatus). Unless otherwise stated all experiments, unidirectional and bidirectional, were carried out in “fixed load” configuration (via the counter-balanced dead weight of the apparatus, Figure 5a). The vertical load was nominally 30N. For the unidirectional experiments the abrasion test was briefly halted at predetermined abrader pass numbers [50, 100, 250, 500 and 1000] and the abraded material debris collected and weighed. Every 10th pass, at the beginning of the new stroke and with the ram stationary, an image of part of the sample surface was captured (7.5mm x 5.5mm). For bi-directional tests, the displacement stroke was 20 mm and the sawtooth waveform was unmodified with a velocity of 35mm/s. 1000 double passes (1000 rightward and 1000 leftward) were performed. No wear debris was collected for weighing. As with the unidirectional experiments, abrasion depth measurements were made with vernier callipers at the end of each test.


125

Fig. 5a Experimental apparatus for abrasion tests. (Rubber testpiece is 200 mm long.)

Figure 5a Experimental apparatus for abrasion tests. (Rubber testpiece is 200 mm long.) (i)

(ii)

4

(a)

8

(b)

5.5 6.8

0.9

10.2

5.5 0.9

R 0.1

6.8 R 0.1

10.2

Fig. 5b Steel blade abraders for (i) unidirectional (ii) bi-directional experiments. g

()

( )

Abrasion track

10.5mm 10.5mm

p

Start

A

90mm

Fig. 5c Diagram showing the area (A, 7.5 x 5.5mm) of abraded surface photographed every 10th pass of the blade abrader in unidirectional tests.

All displacement measurements were based on ram position – no account was taken of compliance or set in the rubber. In order to obtain profiles of the abraded surfaces, slices ~ 0.5mm thick were cut from the rubber blocks using a sharp blade lubricated with detergent solution.

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Elastomers and Components: Service Life Prediction – Progress and Challenges 3 RESULTS AND DISCUSSION

3.1 UNIDIRECTIONAL

Images captured via the digital camera (see 2.2) and force signals were studied. Included in this were abrasion stroke numbers corresponding to changes in types of behaviour as observed in the appearance of the surface or in the force signals denoted ni (force or image). Images of abraded surfaces at different stages of the abrasion process are shown in Figure 1. Generally, experiments were performed under nominally fixed load conditions; the fact that similar pattern “wavelengths” (λ) were obtained under “fixed displacement” conditions indicated that λ was not a function of any (simple) natural frequency of the apparatus. 3.1.1 IMAGE INSPECTION AND ANALYSIS

As abrasion progressed, sequential changes took place in the appearance of the elastomer surfaces (Figure 1). Other authors (Muhr & Roberts 1987, 1992) have recorded the formation of initial pits. The spatial resolution here was insufficient to observe very fine details in the earliest stages. (See also: Fukahori & Yamazaki, 1994a&b; Coveney & Menger, 1999.) The development of apparent pits or craters ~0.1mm in dimension was, however, discernible as early as 40 cycles. Apparent scoring was also seen for NBR and EPDM at the very earliest stages. Roll formation was seen in all cases. Craters were not seen for EPDM, but for all other materials as the craters developed and merged they gradually covered the surface. Eventually, ridges were formed and covered the whole abraded track. Often ridges appeared to emanate from the edges of the blade/track. For all materials tested it was found that Schallamach pattern drift started (n2) as soon as a ridge pattern became established across ~90% of the image (n1 image, Figure 5c and Table 2). Within ~100 cycles of (visual) pattern drift starting, the rate of drift became steady. The formation and drift of the Schallamach pattern were observed for all materials tested except for EPDM which did not form a Schallamach pattern along the main part of the abraded track – although some patterning was evident at the beginning of the abrasion stroke and at the edges of the track. Overall the observations made here regarding the stages of abrasion were consistent with reports by others (Gent, 1989, Muhr & Roberts, 1992): intrinsic small-scale abrasion followed by large scale material removal associated with a drifting Schallamach pattern. By monitoring the leading edge of a ridge in the captured image, by eye with the help of computer-generated “cross hairs”, plots of pattern position against abrasion stroke number were generated. Rates of pattern movement per abrasion stroke or pass [∂x/∂n (image)] are shown in Table 2 together with values for n1 and n2 (image). In places the cross sections of abraded NBR and NR65 (Figure 2) show the clear sawtooth profile associated by Southern & Thomas (1978) with the flap theory; the NR55 shows the occasional sawtooth profile; the abraded NR45 has a very wavy surface but sawtooth profiles are difficult to discern; the surface of the EPDM shows features only on a scale ~0.2mm and smaller. It should be noted, however, that the roots of the flaps did not, for any example viewed, appear to be the sharply delineated crack tips as envisaged in the Southern & Thomas model.


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Table 2 Parameters calculated for materials used in current unidirectional abrasion experiments with estimated errors shown. [λpk: dominant wavelength (of force signals); n1 (force) number of abrasion passes or strokes to formation of quasi-regular force pattern across ~90% of stroke; n1 (image) number of strokes to formation of (visual) Schallamach pattern across ~90% of the examined surface; n2: stroke number at which pattern drift starts; ∂x/∂n: pattern’s lateral drift rate (force signal or image); ∂m/∂n: mass loss per stroke; ρ : density calculated from MRPRA (1984); m1000 or m5000: material loss after 1000 or 5000 strokes of (unidirectional) abrasion; nm2: estimate of stroke number at start of constant ∂m/∂n; θ: “dive” angle derived from ∂m/∂n and ∂x/∂n for force signal or image; ∂r/∂n: total rate of movement of pattern = ∂c/∂n (notional crack growth rate); Fx peak (averaged): averaged (cyclic) maximum horizontal force; “T”: typical notional strain energy release rate calculated from Equations (1)-(4).]

3.1.2 FORCE PLOTS

The force and displacement transducers allowed plots to be made of force (horizontal, Fx, and vertical, Fz) against abrader blade position (x) relative to elastomer testpiece. To give an overall picture of the evolution of force patterns, Fx and Fz were plotted, for unidirectional sliding, as levels of grey against x (as ordinate) and abrader pass number (n) as abscissa. The plots for Fx and Fz were similar in appearance although there was less “noise” on the Fz signal. The (averaged) peak values of Fx were in the range 33 (±18) to 36 (±18) N for NR45, NR55, NR65 and NBR, while for EPDM the value was approximately 20±15N. In Figure 6 greyscale plots of Fz (with the mean value of Fz subtracted) against x and n are shown. Furthermore, Fourier transforms were performed on the force plots for each pass of the blade abrader. In Figure 7 greyscale plots show the harmonic content of Fx as a function of reciprocal wavelength and of pass number.

128

Elastomers and Components: Service Life Prediction – Progress and Challenges Fz − Fz

x

n

Fig. 6a Force (Fz[N]), shown as greyscale, against stroke number (n) and ram position (x [mm] for NR55.

position (x [mm]) for NR55 (unidirectional sliding).

Fz − Fz Fz − Fz

xx

n

Fig. 6b Force (Fz[N]), shown as greyscale, against stroke number (n) and ram position (x [mm] for NBR.

Examination of the force plots and their Fourier analysis indicated that for NR65, NBR and EPDM there was a single dominant wavelength (or narrow range of wavelengths) in the measured forces which lay between 2 and 3 mm. For NR45, late on in the abrasion process there emerged other major Fourier components at other wavelengths. (For NR55, also, there was some suggestion of other wavelengths in the Fx spectrum.) Study by eye of the (photographic) images of the abraded surfaces (Schallamach patterns) pointed to


129

Fz − Fz

x

n

Fig. 6c Force (Fz[N]), shown as greyscale, against stroke number (n) and ram position (x [mm] for NR45.

position (x [mm]) for NR45 (unidirectional sliding).

Fz − Fz

x

n

Fig. 6d Force (Fz[N]), shown as greyscale, against stroke number (n) and ram position (x [mm] for EPDM.

dominant wavelengths which although somewhat smaller were of the same order as those obtained from Fourier analysis of the force signals. As can be seen from Figure 6 and Table 2 the cyclic force patterns emerged at or very near the first pass of the blade abrader (n1 force). The patterns, initially weak, grew in strength but remained essentially stationary at first – indicated by horizontal parallel grey bands in Figure 6. In all cases other than EPDM, force pattern drift started after between ~100 and 300 abrader passes (n2 force) –

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λ-1

n

Fig. 7a Fourier components of force (Fz[N]), shown as greyscale (dark is high) against stroke number (n) and reciprocal wavelength (λ-1 [mm-1]) for NR55.

λ-1

n

Fig. 7b Fourier components of force (Fz[N]), shown as greyscale (dark is high) against stroke number (n) and reciprocal wavelength (λ-1 [mm-1]) for NBR.

indicated by inclined parallel grey bands. Within a further ~100 passes, the drift rate reached a steady value. It was noted, though, that the dominant wavelengths of the force patterns remained unchanged from inception up to and during this transition period – and thereafter in most cases. Also, notwithstanding experimental error, n2 (force) and n2 (image) values were similar. Furthermore the steady drift rates of force pattern and of


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λ-1

n

Fig. 7c Fourier components of force (Fz[N]), shown as greyscale (dark is high) against stroke number (n) and reciprocal wavelength (λ-1 [mm-1]) for NR45.

λ-1

n

Fig. 7d Fourier components of force (Fz[N]), shown as greyscale (dark is high) against stroke number (n) and reciprocal wavelength (λ-1 [mm-1]) for EPDM.

Schallamach pattern (image) were similar. Although EPDM gave cyclic force patterns they did not drift for the 5000 passes of the extended test (except at the turning points). Abrasion was most severe for NR45 and the force plots for it indicated more complex behaviour than was exhibited by the other materials – e.g. for the NR45 there eventually appeared to be at least 2 distinct but co-existing pattern drift rates.

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Prior to, or in the absence of, a clear Schallamach pattern, the increase in force pattern amplitude appears to be associated with surface damage. Similarities in the behaviour of the (visual) Schallamach and the force patterns suggest a close relationship between the two. 3.1.3 MATERIAL LOSS

m

m(EPDM)

Material loss results are shown in Figure 8; totals after 1000 passes, or 5000 for EPDM, m1000, m5000 are shown in Table 2. For all 5 materials there is a period early on where the rate of material loss has not settled to a constant value. An indication of this period, nm2 [strokes], can be found by taking the intercept of the line of approximately constant material loss per pass (∂m/∂n) with the line of n = 0. For NR45 nm2 is 55±10 (strokes), for EPDM nm2 was 915±10. For NR65, NR55 and NBR nm2 ranges only from 161±10 to 198±10 (Table 2). For the natural rubber materials, material loss rate depends inversely on hardness, with NR45 losing material almost twice as quickly as NR65. The loss rates for NR55 and NR65 are, however, quite similar. NBR loses material at about half the rate of the natural rubber sample of similar hardness (NR55). The rate of material loss for the EPDM was 60 times lower than that for the NR55 – despite the fact that both materials were of similar hardness. For the EPDM there is a suggestion that the mass loss rate may not have settled to a steady value even after 5000 passes. Even if EPDM is excluded material-material variation of n2 (and nm2) was by a factor of ~3; if EPDM is included the factor was ~15 plus. In our experiments, with the exception of EPDM and despite experimental error, the onset of (rapid) material loss (n m2) did appear to coincide, approximately, with the formation of the Schallamach pattern (n1 image) and the onset of pattern drift (n2). For materials other than EPDM material was lost at ~1µm per pass; these figures are orders of magnitude higher than average figures for loss per revolution for tyres on automobiles – reflecting the relatively high stresses applied in our experiments. The EPDM lost material at ~40nm per pass in our experiments.

n Fig. 8 Plot of mass loss m (g) against stroke number (n) for unidirectional abrasion.


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3.1.4 GENERAL DISCUSSION FOR UNIDIRECTIONAL EXPERIMENTS

For four out of the five materials a clear Schallamach abrasion pattern developed within a few hundred abrasion passes (Figure 1). ( In contrast, for the EPDM material, no pattern was apparent even after 5000 passes.) Flaps were ultimately observed. However the progressive development and detailed appearance of the flaps (e.g. often thin leading edges, no sharp root crack apparent) was difficult to reconcile with the Southern & Thomas (1978) model (q.v. Figure 3). Also, because the force patterns are present from the beginning of the scraping there is a strong suggestion that the dominant wavelengths of the Schallamach pattern have their origin in non-destructive abrader-elastomer interactions such as cyclic hyperelastic-friction-force behaviour (“stick-slip”, “bow-wave” cycles). It seems likely that in Schallamach abrasion, the ab initio stick-slip behaviour leads to an intensification of intrinsic abrasion damage processes which in turn sculpt the surface leading to further intensification. Dive angles (θ) were calculated from (force and visual) pattern drift rates and wear rates [Southern & Thomas, 1978; Equation (4) and Table 2], whence the notional strain energy release rate (T) and the notional crack growth rate (∂c/∂n) were found. Except for the EPDM all values of θ lay in a narrow range 8-15° [compared to the range of 115° reported by Southern & Thomas (1978) for their experiments]. The current experiments were performed at higher values of force per unit width than those of Southern & Thomas (1978) and hence at higher values of notional T. (The central values in) our results for filled NBR, NR55 and NR65 appear below the ∂c/∂n range given by extrapolating the Southern & Thomas (1978) values for abrasion or crack growth for (unfilled) NBR, isomerised NR (Figure 4a) and normal NR (Figure 4b); these findings point once more to the effect of filler. Our value of notional ∂c/∂n for NR45 lies near a straight line extrapolated from the Southern & Thomas (1978) results for abrasion of unfilled normal NR (Figure 4b); this result is as expected since the NR45 was a low modulus material with a low loading of relatively large particle-size filler – i.e. the effect of filler is likely to be minor. Our values of notional ∂c/∂n for NR45, NR55 and NR65 lie between the straight line extrapolations of (normal) NR data for apparent ∂c/∂n (from abrasion) and of ∂c/∂n (from fatigue crack growth) given by Southern & Thomas (1978) [Figure 4b]. Although Southern & Thomas (1978) suggest a relationship between horizontal force (Fx) and Schallamach pattern wavelength (λ) our data indicates that no general intermaterial relationship exists between these two variables (Fig 9(a)). Our data supports the view of Medalia et al (1992) that a good correlation exists between wear rate (∂m/∂n) and flap thickness (h) (Fig 9(b)) but that ∂m/∂n is not closely related to λ (Fig 9(c)). As pointed out by Gent & Pulford (1983) there is an inverse relationship between rubber hardness and λ (Fig 9(d)). Our data also suggests a direct relationship between pattern drift rate and wear rate (Fig 9(e)). EPDM was exceptional as it did not exhibit a general Schallamach pattern. This may have been because of the prevalence of smearing abrasion damage, which (as suggested by Gent & Pulford, 1983) may in turn be associated with the strong tendency of EPDM materials to terminate free-radical reactions without cross-linking. However, the fact that Schallamach patterns were observed at the extremes of the abrasion track for the EPDM shows that there are conditions under which pattern abrasion occurs even for this material.

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Elastomers and Components: Service Life Prediction – Progress and Challenges (a)

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60

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∂x / ∂n Fig. 9 Plots showing relationship between (a) horizontal force Fx [N] and pattern wavelength λ [mm], (b) mass loss rate, ∂m/∂n [mg/cycle] and flap thickness h [mm], (c) ∂m/∂n and λ, (d) IRHD and λ, (e) ∂m/∂n and pattern drift rate ∂x/∂n [µm/cycle].

Table 3 Depths of abrasive wear (in mm) for unidirectional and bi-directional sliding. [Estimated error ±0.1mm.] Constant load of 30N, 90mm stroke, 27mm/s rate for unidirectional sliding [1000 servohydraulic ram cycles, except *5000]; and 30N load, 20mm stroke, 35mms -1 (Menger, 2001) for bi-directional sliding [1000 servohydraulic ram cycles] .


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Sliding direction NR45

NR55

NR65 NBR

EPDM 0

mm

20

Fig. 10 Cross-sections of bi-directional abrasion test pieces (30N load, 35mm/s sliding velocity, 1000 servohydraulic ram cycles each of 20mm stroke).

3.2 BI-DIRECTIONAL

If unidirectional and bi-directional abrasion loss results were considered on the basis of equal numbers of cycles of the hydraulic ram, bi-directional abrasion gave increased abrasion loss (Table 3). However, for bi-directional conditions the rubber surface received two passes of the blade per cycle. Thus the unidirectional abrasion depths in Table 3 apply to 1000 passes and the bi-directional test depths to 2000 passes. Consequently all materials with the possible exception of NR55 do appear to show a reduction in the abrasive wear per pass for bi-directional abrasion relative to unidirectional abrasion, but the reduction is not major. Figure 10 shows cross-sections for bi-directional abrasion tests. The abraded NR45 exhibited a clear wave-like pattern somewhat similar to that observed for unidirectional sliding. For NR55 the surface exhibited roughness of similar magnitude to that obtained for unidirectional sliding although there was little evidence of sawtooth features. For the NR65 and NBR the surface appeared less rough than for the unidirectional sliding. Abrasion of NBR was accompanied by particularly noticeable roll formation and material loss was much greater towards the turning points of the stroke. For EPDM very little material was removed except near the turning points of the stroke.

4 CONCLUSIONS The technical importance of abrasion of elastomers is matched by the difficulty of the subject. It is widely believed that under conditions of quite severe tangential stress, fatigue crack-growth-related processes dominate – a view supported by the work of Thomas and co-workers (Champ et al, 1974; Southern & Thomas, 1978). If there is unidirectional abrasion under such conditions, Schallamach patterns often occur and wear rates are high. The (Shallamach pattern) model of Southern & Thomas (1978) is in accord with some experimental observations but not others while the outline models put forward by Fukahori & Yamazaki (1994a&b, 1995) and by Gerrard & Padovan (2002) remain to be fully

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explored and developed. There are strong indications that Schallamach abrasion patterns result from intrinsic (i.e. patternless) abrasion processes intensified by gross stick-slip behaviour – the wavelength of which is inversely related to the rubber hardness. Under milder or non unidirectional conditions, such as those typically occurring on the tread of a radial tyre, there is intrinsic abrasion. Interestingly, when account is taken of the fractal nature of the road surface, the normal contact stresses are thought to be rather high (~30 MPa) at the µm scale. Intrinsic abrasion can be smearing or non-smearing (particulate). Gent & Pulford (1983) put forward convincing arguments for the role of mechano-chemical degradation in intrinsic abrasion, however it may still be premature to rule out the role of oxidation accelerated by high temperatures. (Carbon black filled) EPDM materials showed an exceptionally strong tendency towards smearing abrasion in Gent & Pulford’s (1983) experiments and away from Schallamach pattern abrasion in our (generally more severe) experiments. However Schallamach pattern abrasion can occur in some circumstances even for EPDM. Remaining questions, and the inability to always predict the conditions under which a given type of abrasion will occur for a given material, highlight the continuing need for a comprehensive quantitative theory of rubber abrasion.

ACKNOWLEDGEMENTS The authors acknowledge the contributions of Christian Menger and Anthony Soo in aspects of the experimental work.

REFERENCES Arnold JC (1997) “Impact of small particles onto rubber surfaces at glancing angles” J Appl Polym Sci, 64, 2199-2210. Arnold JC & Hutchings IM (1992) “A model for the erosive wear of rubber at oblique impact angles” J Phys D: Appl Phys, 25, A222-A229. Azura AR & Thomas AG (2005) “Effect of heat ageing on crosslinking, scission and mechanical properties”, (This Volume). Bristow GM & Watson WF (1963) “Mastication and mechanochemical reaction of polymers” in The Chemistry and Physics of Rubber-Like Substances, L Bateman (ed), Maclaren, London, pp 417-447. Brydson JA (1978) Rubber Chemistry, Applied Science, Barking. BSI (British Standards Institution, 1987) “Method of testing vulcanized rubber. Determination of abrasion index.” BS903 part A9. Champ DH, Southern E & Thomas AG (1974) “Fracture mechanics applied to rubber abrasion” Coatings, Plast, Prep (Am Chem Soc), 34 (1), 237-243. Coveney VA & Menger C (1999) “Initiation and development of wear of an elastomeric surface by a blade abrader” Wear, 233-235, 702-711. Coveney VA & Menger C (2000) “Behaviour of model abrasive particles between a sliding elastomer surface and a steel counterface” Wear, 240, 72-79. Daley J (2005) “Assessment of life prediction methods for elastomeric seals – a review”, (This Volume).


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Dannenberg EM (1986) “Carbon black treadwear ratings from laboratory tests” Rubber Chem Technol, 59, 497-511. Fukahori Y & Yamazaki H (1994a) “Mechanism of rubber abrasion Part I: abrasion pattern formation in natural rubber vulcanizate” Wear, 171, 195-202. Fukahori Y & Yamazaki H (1994b) “Mechanism of rubber abrasion Part II, General rule in abrasion pattern formation in rubber-like materials”, Wear, 178, 109-116. Fukahori Y & Yamazaki H (1995) “Mechanism of Rubber Abrasion. Part 3: How is friction linked to fracture in rubber abrasion?”, Wear, 188, 19-26. Furukawa J (1996) “Chemical aspects concerning the friction and abrasion of rubber” Bull Chem Soc Japan, 69, 2999-3006. Gent AN (1989) “A hypothetical mechanism for rubber abrasion” Rubber Chem Technol, 62, 750756. Gent AN & Pulford CTR (1978) “Wear of steel by rubber” Wear, 49, pp 135-139. Gent AN & Pulford CTR (1983) “Mechanics of rubber abrasion”, J Appl Polym Sci, 28, pp943-960. Gerrard DP & Padovan J (2002) “The friction and wear of rubber. Part 1: effects of dynamically changing slip direction and the damage orientation distribution function” Rubber Chem Technol, 75, 29-48. Gerrard DP & Padovan J (2003) “The friction and wear of rubber. Part 2:micro-mechanical description of intrinsic wear” Rubber Chem Technol, 76, 101-121. Grosch KA (1996) “The rolling resistance, wear and traction properties of tread compounds”, Rubber Chem Technol, 69, 495-568. Heinrich G (1997) “Hysteresis friction of sliding rubbers on rough and fractal surfaces” Rubber Chem Technol, 70, 1-14. ISO (International Standards Organisation, 1985) “Rubber – determination of abrasion resistance using a rotating cylindrical drum device” ISO 4649. Jacobson K (1999) “Oxidation of stressed polymers as studied by chemiluminescence”, PhD Dissertation, KTH Stockholm, ISBN 91-7170-440-x. Kluppel M & Heinrich G (2000) “Rubber friction on self-affine road tracks” Rubber Chem Technol, 73, 587-606. Lake GJ & Lindley PB (1964) “Ozone cracking, flex cracking and fatigue of rubber, part 2, technological aspects” Rubber Journal, 146, 30-36 & 39. Medalia AI, Alesi AL & Mead JL (1992) “Pattern abrasion and other mechanisms of wear of tank track pads” Rubber Chem Technol, 65, 54-175. Medalia AI & Newton (1994) “Effects of carbon black on abrasion and treadwear”, Kautschuk Gummi Kunststoffe, 47, 364-368. Menger C (2001) “Behaviour of sliding seals in abrasive fluids” PhD thesis, University of the West of England, Bristol, UK. Mori K, Oishi Y, Hirahara H, Kanae K, Iwabuchi A, Tutumi A & Yamabe H (1993) “Effects of molds on the surface free energy and friction coefficient of vulcanizates”, Kobunshi Ronbunshu, 50, 629-635. Mori K, Kaneda S, Kanae K, Hirahara H, Oishi Y& Iwabuchi A (1994) “Influence on friction forces of adhesion force between vulcanizates and sliders”Rubber Chem Technol, 67, 797-805. Muhr AH, Pond TJ & Thomas AG (1987) “Abrasion of rubber and the effect of lubricants”, J de Chimie Physique, 84, Part 2, 331-334. Muhr AH & Roberts AD (1988) “Friction and wear” in Natural Rubber Science and Technology, AD Roberts (ed), Oxford University Press, Oxford, 773-819.

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Muhr AH & Roberts AD (1992) “Rubber abrasion and wear” Wear, 158, 213-228. MRPRA (1984) Natural Rubber Formulary and Property Index, Malaysian Rubber Producer’s Research Association, Hertford (ISBN 0-9504401-3-2). Newton EB, Grinter HW and Sears DS (1961) “The Pico laboratory abrasion test” Rubber Chem Technol, 34, 1-15. Persson BNJ (2000) Sliding Friction – Physical Principles and Applications 2nd Edition, Springer (ISBN 3 540 67192-7) Persson BNJ & Tosatti E (2000) “Qualitative theory of rubber friction and wear”, J Chemical Physics, 112, 2021-2029. Persson BNJ (2004) Presentation and discussion at and shortly following Tire Technology Expo 2004, Stuttgart, March. Rivlin RS & Thomas AG (1953) “Rupture of rubber, Part 1, Characteristic energy for tearing”, J. Polym Sci, 10, 291-318. Rorrer RAL (2000) “A historical perspective and review of elastomeric stick-slip” Rubber Chem Technol, 73, 486-503. Schallamach A (1958) “Friction and abrasion of rubber”, Rubber Chem Technol, 31 (5), 982-1014. Smith RN & Veith AG (1982) “Electron microscopical examination of worn tire treads and tread debris”, Rubber Chem Technol, 15, 469-482. Southern E & Thomas AG (1978) “Studies of rubber abrasion” Plastic and Rubber: Materials and Applications, 3, 133-138. Stupak PR & Donovan JA (1988) “Fractal analysis of rubber wear surfaces and debris” J Materials Science, 23, 2230-2242. Stupak PR, Kang JH & Donovan JA (1990) “Fractal characteristics of rubber wear surfaces as a function of load and velocity” Wear, 141, 73-84. Veith AG (1986) “The most complex tire-pavement interaction: tire wear” in The Tire Pavement Interface, MG Pottinger & TJ Yager (eds), ASTM publication code no 04-929000-27, 125-158. Westermann S (2004) Presentation and discussion at and shortly following Tire Technology Expo 2004, Stuttgart, March. Williams RL & Cadle SH (1978) “Characterization of tire emissions using an indoor test facility” Rubber Chem Technol, 51, 7-25.

CHAPTER 9

Life Prediction of O-rings Used to Seal Gases VA Coveney and R Rizk Engineering, Medicine and Elastomers Research Centre, University of the West of England, Bristol, UK

SYNOPSIS Elastomeric O-ring seals perform essential functions in domestic equipment, transport and the energy industries, often over many years and in environments which are demanding in terms of fluid exposure, temperature or both. In this chapter a step towards improved service life prediction of these components is described. The literature and work performed by the authors on pertinent aspects of the long-term behaviour of elastomers including stress relaxation and set are discussed, as are experiments to study seal failure directly. It is concluded that current methods for life prediction may not be appropriate in all cases. Alternative approaches are suggested.

1 INTRODUCTION 1.1 BACKGROUND

Sealing devices are used almost everywhere; from simple bottle caps to rocket boosters their aim is the same: to prevent or restrict leakage. Of course, the importance of these devices varies according to the application. Often they are required to accommodate dimensional and pressure changes in demanding environments, across wide extremes of temperature, or in fluids which are challenging for many elastomers. For the elastomeric material used, a balance must therefore be struck between environmental requirements, such as the temperature and surrounding fluid, and mechanical requirements, for example strength and elasticity. Also, in some applications, failure or premature replacement can have serious consequences or can be extremely difficult and expensive. There is therefore a need for reliable and accurate life prediction methods. Over the last quarter century, design tools such as finite element analysis (FEA) have begun to be used in seal design and sizing (Daley & Mays, 1999). However, despite the importance of many seals, service life prediction methods are generally primitive, relying on a combination of trial-and-error and single measures such as compression set or stress 141

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relaxation. More recently work has been done to incorporate material relaxation into finite element analysis for seal design (George et al, 1987; Metcalfe et al, 1992; Ho, 1992). As in other areas of lifetime prediction, current methods of seal failure prediction are subject to very large overestimation or underestimation (Raines & Callahan, 1990). In this chapter the emphasis will be on how seals actually fail. 1.2 CURRENT METHODS OF O-RING LIFE PREDICTION

Central to current methods (Parker & Raines, 1989; Fulmer et al, 1994; Heeney & Metcalfe, 2000) are the two related parameters: stress relaxation and compression set. The stress relaxation (Rs) for a given (compression, tensile or shear) testpiece held at constant deformation is the decrease with time of the force exerted by the testpiece. Usually, the reduction in force (∆F) is expressed as a fraction or a percentage of the reference force (F1) and usually the reference force is the force exerted by the testpiece one minute after the deformation is suddenly applied (BS903: Part A42, 1983; ISO 3384, 1986; ISO 6056, 1987).

(1) Stress relaxation can arise from a combination of physical (e.g. viscoelastic) and chemical (e.g. crosslinking) effects; the former are largely recoverable over timescales of hours at moderate temperatures while the latter are not (Fuller et al, 1988; Coveney & Muhr, 1992). For crosslinked elastomers operating at elevated temperatures over extended periods, chemical relaxation dominates. When the deforming constraint, i.e. the applied deformation u a , is removed from a testpiece which has undergone substantial chemical relaxation, much of the deformation will remain as a residual deformation ur. This is the set, defined as

(2) with S(%) = 100 S. The residual deformation ur is generally measured half an hour after the constraining deformation is removed (BS903: Parts A6 & A39, 1983; ISO 815, 1986; ISO 1653, 1986). It has been pointed out by a number of authors (Birley et al, 1986; Clinton & Turner, 1990; Raines & Callahan, 1990) that for a given elastomeric material at a given temperature, stress relaxation differs with both the magnitude and the mode of deformation of the testpiece, i.e. compression, tension or shear. Also, deformation is often not constant with time in service, and deformation history can have a profound effect on relaxation (Birley et al, 1986; Derham & Thomas, 1977). Often, the concepts of stress relaxation and compression set are applied to the seal as a whole or to a scaled-down physical model of it. Seal failure, under either real-time or accelerated conditions, is then associated either with the relaxation to zero of the force exerted by the (constant) deformation or with the approach to almost 100% compression set.

Life Prediction of O-rings Used to Seal Gases

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Many seals are required to have a service life of years, sometimes of many years. Routine developmental testing of materials, or whole seals, on such time scales is not viable, so accelerated testing, generally at temperatures above those encountered in service, is widely adopted. The Arrhenius rate law is then commonly used to find equivalent time period and absolute temperature pairs (τ1, T1) and (τ2, T2):

(3) Here 1/τ1 and 1/τ2 are proportional to reaction rates, R is the universal gas constant (1.987 x 10-3 kcal mole-1 K-1 or 8.314 J mole-1 K-1) and A is the molar activation energy of the reaction (Albihn, 2005). In order to make more efficient use of test data Heeney & Metcalfe (2000) advocate the use of, Arrhenius-based, time-temperature shifted property-time curves. A shortcoming of the aforementioned approaches is that seal failure, i.e. leakage, is simply associated with an arbitrary or a heuristic value of compression set or stress relaxation; failure mechanisms are not considered in detail. The purpose of the work described in this chapter is to study failure mechanisms in Oring seals, starting with a forensic examination of seals which have and have not failed. 1.3 TOWARDS A NEW UNDERSTANDING OF O-RING SEAL BEHAVIOUR

In our study we aimed to create circumstances resembling those seen by O-ring seals in service. Conditions where oxidation could take place were a particular focus of the study. Two types of experiments were performed. (i) Large-scale simulation experiments in a transparent apparatus to give insight into the mechanical behaviour of O-ring seals. (ii) Experiments on smaller seals to study the ways in which ageing can lead to seal failure. In the ageing experiments, higher temperature was the only accelerating factor; measurements were then carried out after different periods of time to build up a picture of O-ring seal behaviour.

2 LARGE SCALE PHYSICAL SIMULATION 2.1 EXPERIMENTAL – MATERIALS, APPARATUS, METHODS

An important aspect of seal failure is how, physically, the leakage takes place. Thus, the aim of this first experiment was to visualise the mode of leakage in a pressurised component sealed by means of an ‘O’ ring seal. The apparatus consisted of two transparent polymethylmethacrylate flanges, in which a large-scale soft silicone (VMQ – G ≈ 0.02 MPa) ‘O’ ring seal (214 mm OD / 25 mm CSD1) 1

OD: Outer Diameter. CSD: Cross Sectional Diameter.

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Fig. 1 Large scale physical simulation – test apparatus. (Flange thickness: 12mm.)

was exposed to a modest air pressure at room temperature (Figure 1). The dimensions and material characteristics of the scaled seal were selected by means of mathematical calculation and finite element (FE) modelling. The low modulus of the elastomer meant that relatively low pressures could be used to bring about major seal deformation, such as occurs at much higher pressures for elastomers with more ‘normal’ moduli. 2.2 EXPERIMENT 1, RESULTS

Before applying the pressure, the seal had a symmetrical shape under 12% “squeeze”1. The upper and lower footprints were each 11 mm wide [Figure 2(a)]. When the pressure was increased to 6.9 kPa (1 psi) above atmospheric, very significant radial deformation took place and the soft silicone was pushed to the upper corner, displacing the air through the gap. However, no slippage occurred [Figure 2(b)]. The upper footprint width increased to 14 mm but the lower one was unchanged. At 41.4 kPa (6 psi), the silicone was deformed further outwards towards the groove wall, and peeling took place on the pressurised side of the seal (≈ 3 mm). On the outer side, the upper footprint reached the gap, and the lower footprint advanced by 1 mm of new contact along the lower surface [Figure 2(c)]. The situation remained stable until a pressure difference of approximately 1 bar (103.5 kPa, 15 psi) was reached; at this point the seal was extruded into the gap [Figure 2(d)]. No leakage took place. To summarise, as the pressure increased, the seal filled the unpressurised spaces by deforming and rolling along (peeling and adhering to) the flange surfaces; no slippage took place. 2.3 EXPERIMENT 2, RESULTS

The experiment was next carried out using the same seal under only 2% “squeeze” [Figure 3(a)]. The intention was to bring about conditions similar to those occurring 1

% “squeeze” = [1-(h/d0)] x 100 where h is the depth of the rectangular groove and d0 is the seal’s cross sectional diameter.


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Fig. 2 Large scale physical simulation – behaviour under 12% “squeeze”. Pressure differences across the seal as follows: (a) 0, (b) 6.9 kPa (1 psi), (c) 41.4 kPa (6 psi), (d) 103.5 kPa (15 psi).

Fig. 3 Large scale physical simulation – behaviour under 2% “squeeze”. Pressure differences across the seal as follows: (a) 0, (b) 31 kPa (4.5 psi), (c) 103.5 kPa (15 psi).

when there is a high percentage compression set in a practical sealing situation. In spite of the low compression level no leakage was observed and a pressure activated sealing mechanism took place when a pressure of 31 kPa (≈ 4.5 psi) was reached: the upper contact surface reached the gap and the seal lost all contact with the bottom flange [Figure 3(b)]. Perfect sealing followed and, once again, the soft silicone seal did not fail [Figure 3(c)]. No slippage was observed at the top surface at any stage. 2.4 INITIAL DISCUSSION

Although the conditions in the large-scale physical simulations were simpler than in many real service environments, the experiments were felt to be informative, enabling a number of lessons to be drawn.

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Firstly, when a pressure difference exists across it, an O-ring seal deforms asymmetrically at the contacts with the “upper” and lower flanges. This observation was confirmed by examination of a large number of deformed aged seals – see below. It seems that once equilibrium has been established between the seal and the trapped fluid at the lower outer perimeter in terms of pressure, friction, diffusion, adhesion, etc, the latter acts as a fluid cushion impeding total contact between the O-ring and the sealing groove. Note that quite different behaviour takes place near the gap at the upper, outer perimeter (Figure 2), where the pressure gradient causes extrusion of the rubber. As a result of the fluid cushion effect, pressure is exerted from both sides and reduces the lower contact patch. Therefore, if the percentage “squeeze” is small, as in a seal with high compression set, the O-ring can leave the lower surface completely – pushed towards the gap by the pressure difference if this is high – and can still seal. The conformability or softness of the rubber might be expected to be a key pre-requisite of such behaviour.

3 ACCELERATED AGEING – EXPERIMENTS ON NBR (NITRILE) O-RING SEALS IN AIR 3.1 APPARATUS AND MATERIALS

The aim of these experiments was to determine the change in the properties (hardness, compression set, geometry) of elastomeric seals when exposed to heat and air pressure. A number of nominally identical acrylonitrile butadiene (NBR) O-ring seals (52 mm OD, 7 mm CSD) were used in the experiments. [The NBR was a medium acrylonitrile butadiene nitrile rubber with a hardness of 80 IRHD (international rubber hardness degrees) and normal carbon black filler and antioxidant levels.] The seals were subjected to 15% “squeeze” in apparatuses with stainless steel flanges and heated to an approximate temperature of 120°C (Figure 4). Pressurisation (by air) was maintained at 4MPa (580 psi). After various periods of time, the seals were taken out and measurements were made of dimensional properties such as shape and compression set, and of material properties such as hardness. One set of seals was aged until failure.

80 mm 52 mm

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Figure 4 Accelerated ageing –experimental apparatus Fig. 4 Accelerated ageing – experimental apparatus.


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3.2 COMPRESSION SET – METHOD, RESULTS AND INITIAL DISCUSSION 3.2.1 METHOD

Successive measurements of the level of compression set reached by the seals after different periods of time were carried out in two different ways. • Method I: seals taken out from the hot apparatus (≈ 120°C) and cooled down afterwards. • Method II: seals left to cool down to ambient temperature (≈ 20°C) in apparatus before removal. All the measurements were carried out 30 minutes after the removal of the seal from the apparatus, noting that for method I, the cooling time was part of the 30 min. In addition to the standard method II (method IIa), some method II seals were reheated outside the apparatus and measured at the elevated experimental temperature (method IIb). Some were then recooled and remeasured once they had again reached ambient temperature (method IIc). 3.2.2 RESULTS

Typical results are shown in Figures 5 & 6.

Fig. 5 Accelerated ageing of NBR O-ring seals at 120°C and 40 bar air pressure – comparison between methods I & IIa: compression set (CS) against ageing time (t).

Fig. 6 Accelerated ageing – effect of reheating, method II: compression set (CS) against ageing time (t).

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3.2.3 DISCUSSION

Although both sets of the measurements in Figure 5 were taken at ambient temperature, the results were quite different in the two cases. The sequence of events obviously has an important influence. Furthermore, the difference between the temporary physical set which is partially or totally recoverable on warming, and the essentially permanent chemical set was clear: in the early stages physical effects are larger, but after longer periods of ageing, chemical changes are dominant. In other words, the changes occurring in the elastomeric material gradually reduce its ability to recover; eventually the only remaining pseudorecovery effect, of a few percent, appears to be thermal expansion (Figure 6). 3.3 SEALING FUNCTION AND CHANGES IN MATERIAL PROPERTIES – METHOD, RESULTS AND INITIAL DISCUSSION 3.3.1 METHOD AND RESULTS

The seals were subjected to conditions as described in 3.1 for differing periods of up to 2000 hours before removal. When taken out from the ovens, the steel flanges were left to cool down to the ambient temperature (≈ 20°C) before the seals were removed and measurements were carried out 30 minutes afterwards (method IIa – see 3.2.1). In addition to dimensional measurements, IRHD hardness measurements were carried out on the seals’ outer surfaces and on cross-sectional surfaces following sectioning. Using a Wallace micro indentation tester, IRHD maps were obtained (Figure 7). In many cases it was noticeable that the aged seals adhered to the upper flange surface and had to be prised off, but this was not the case at the lower steel surface.

Fig. 7 Accelerated ageing – micro hardness (IRHD) cross-sectional profiles (at ambient temperature) % compression set figures (by method IIa) are shown.

3.3.2 INITIAL DISCUSSION

The hardness maps (Figure 7) show the infiltration of oxygen into the elastomer which creates a hardening “front”. Since the diffusion is related to the concentration (i.e. the partial pressure) of oxygen in contact with the seal, the progression of air (accompanying the peeling or lifting off of the seal) along the upper and lower contact faces can be detected. A salient finding from the accelerated ageing experiments was that the O-ring seals continued to seal, not only beyond the standard failure criterion of 100% compression set at ambient temperature (method IIa), but also above that permanent set level at the elevated


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experiment temperature. Only when the hardness at the upper contact surface reached 99 IRHD did leakage occur.

4 ADDITIONAL ACCELERATED AGEING EXPERIMENTS 4.1 NITRILE O-RING SEALS WITH COMPRESSED NITROGEN

Experiments using a larger apparatus (Rizk, 2002) were performed at 120ºC with nitrogen on the high pressure (inner) side (0-4 MPa above atmospheric pressure) and air at normal atmospheric pressure on the exterior. Similar experiments were performed using compressed air, enabling direct comparisons to be made. It was found that it took over 5 times longer for the O-ring seal to fail with compressed nitrogen than with compressed air. In the compressed nitrogen case, hardening “radiated” from the outer surface strip of the seal exposed to air; this reconfirmed the key role played by oxidation. 4.2 SILICONE O-RING SEALS WITH COMPRESSED AIR

Further experiments were performed with the apparatus as shown in Figure 4 at a temperature of approximately 195ºC with air at up to 4 MPa (580 psi) on the high pressure (inner) side. Despite significant cracking of the elastomeric material a good seal was maintained until about 550 hours of ageing. It was deduced that the probable leakage route was underneath the seal and up along the outer sidewall.

5 GENERAL DISCUSSION Taken together, the results from the large-scale physical simulations and from the accelerated ageing experiments suggest that O-ring seals may leak in quite different ways in different situations. In cases where the pressure difference across the seal is very low, the simple, essentially elastic, interaction between flange, O-ring and groove will dominate. In such circumstances seepage may occur as compression set approaches 100%. At higher sealing pressures, depending on the dimensions and hardness of the seal, the importance of pressure activation has been previously discussed in relation to many sealing situations (Metcalfe et al, 1992). However, its possible importance in relation to seal failure has rarely been highlighted. The present work, involving large-scale experiments and ageing studies, emphasises that the forces exerted by the sealed fluid must be considered together with (visco) elastic forces and deformations acting within the O-ring and at the contact with the counterface. It is also noted that appreciable (≈1 MPa, 145 psi) adhesion can sometimes occur at the rubber-steel interface. In some circumstances, then, effective sealing can continue beyond 100% compression set of the seal. Modes of failure which can be envisaged include those involving the following. (a) Hardening of the rubber (as observed), to the point where intimate contact cannot be maintained with a hard surface of given roughness (Kuran et al, 1994). However, provided the seal is undisturbed, high hardness may be tolerable.

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(b) Circumferential shrinkage and stiffening of the O-ring combined with high compression set to the point where, for a given modulus, fluid pressure and geometry, the O-ring no longer reaches the sealing gap at all points. (c) Rupture or perforation of the rubber. Studies to elucidate and quantify aspects (a)-(c) are ongoing.

6 CONCLUSIONS In experiments ranging from large-scale physical models to more realistic ageing tests, asymmetrical behaviour has been observed in O-ring seals. It has been found that compression set is not always a reliable and suitable criterion to indicate seal failure. Rather, mechanical as well as chemical factors need to be considered in their totality.

ACKNOWLEDGEMENTS The authors wish to thank Dr MA Keavey for useful discussions.

REFERENCES Albihn P (2005) “The 5-year accelerated ageing project for thermoset and thermoplastic elastomeric materials; a service life prediction tool”, (This Volume). Birley AW, Fernando KP & Tahir M (1986) “Appraisal of the current standards for stress relaxation measurements in compression for rubber”, Polymer Testing, 6, 85-105. BS903, Part A6 (1983) “Methods of testing vulcanized rubber part A6 – Determination of compression set at normal and high temperatures”, British Standard. BS903, Part A39 (1983) “Methods of testing vulcanized rubber part A39 – Determination of compression set at low temperatures”, British Standard. BS903, Part A42 (1983) “Methods of testing vulcanized rubber part A42 – Determination of stress relaxation”, British Standard. Chapman AV & Porter M (1988) “Sulphur vulcanization chemistry” page 568, Chapter 12 in Natural Rubber Science and Technology, AD Roberts (ed), 511-620. Clinton RG & Turner JE (1990) “Long-term compression effects on elastomeric O-ring behaviour” AIAA/ASME/ASCE/AHS/ASC 31st Structures, Structural Dynamics and Materials Conference, 2-4 April, 53-61. Coveney VA & Muhr AH (1992) “Design of elastomer-based engineering products” in Concise Encyclopaedia of Polymer Processing and Applications, PJ Corish (ed), Pergamon, Oxford, 180-191. Daley JR & Mays S (1999) “The complexity of material modelling in the design optimisation of elastomeric seals” in Finite Element Analysis of Elastomers, D Boast & VA Coveney (eds), Professional Engineering Publishing, London, 119-128. Derham CJ & Thomas AG (1977) “Creep of rubber under repeated stressing” Rubber Chem & Technol, 50, 397-402. Fuller KNG, Gregory MJ, Harris, JA, Muhr AH, Roberts AD & Stevenson A (1988) “Engineering use of natural rubber”, page 895, Chapter 19 in Natural Rubber Science and Technology, AD Roberts (ed), Oxford University Press, Oxford, 892-937.


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Fulmer MS, Leyden JJ & Pannikottu A (1994) “Relaxation phenomena of various classes of thermoplastic elastomers exposed to severe underhood service conditions” 146th Meeting of the Rubber Division, American Chemical Society, Conference Proceedings, Paper 27, Denver, Colorado. George AF, Strozzi A & Rich JI (1987) “Stress fields in a compressed unconstrained elastomeric Oring seal and a comparison of computer predictions and experimental results.” Tribology International, 20 (5), 237-247. Heeney PL & Metcalfe R (2000) “A new methodology for thermal aging of elastomeric materials and sealing effectiveness of aged O-rings” – presented at the Technical Meeting on Environmental Qualification (EQ) of Nuclear Power Plant Equipment, EPRI, EQDB and NUGEA, Florida, November. Ho THET (1992) “Theoretical and computation modelling of polymer seal life” PhD Thesis, Cranfield Institute of Technology. ISO Standard 815 (1986) “Vulcanized rubbers – Determination of compression set under constant deflection at normal and high temperatures”. ISO Standard 1653 (1986) “Vulcanized rubbers – Determination of compression set under constant deflection at low temperatures”. ISO Standard 3384 (1986) “Rubber, vulcanized – Determination of stress relaxation in compression at ambient and at elevated temperatures”. ISO Standard 6056 (1987) “Rubber, vulcanized or thermoplastic – Determination of compression stress relaxation (rings)”. Kuran S, Gracie BJ & Metcalfe R (1994) “Low pressure sealing integrity of O-rings based on initial squeeze and counterface finish”, Tribology Transactions, 38 (2), 213-222. Metcalfe R, Baset SB & Kuran S (1992) “Contact hydraulics in the sealing footprint – effects on deformation, leakage and friction of soft seals” Atomic Energy of Canada Ltd, Chalk River labs, Ontario, Proc 13th Int Conf on Fluid Sealing, 655-669. Parker BG & Raines CC (1989) “New life prediction technique tests seals in severe service environments” Elastomerics, 20-22. Raines CC & Callahan DM (1990) “Pitfalls of severe environment testing” Cameron Elastomer Technology Inc. – Corrosion 90, Paper 437 – Las Vegas, Nevada, April. Rizk R (2002) “Prediction of the remanent life of elastomer O-ring seals” PhD Thesis, University of the West of England, Bristol.

CHAPTER 10

Stress-Induced Phenomena in Elastomers, and their Influence on Design and Performance of O-Rings GJ Morgan, RP Campion and CJ Derham Materials Engineering Research Laboratory (MERL) Tamworth Road, Hertford,UK

SYNOPSIS Elastomeric seals rely on the maintenance of sealing force to perform their function in resisting the passage of fluid past them. This force arises from stored energy based on stresses induced by being compressed into the sealing housing. However, several other factors relating to these and other stresses can affect long term seal performance and are considered here. The presence of stress in an elastomer can itself cause accelerated ageing and consequent changes in properties; tests with typical filled fluorocarbon elastomers (FKMs) support this statement. Measurements of transient effects relating to the changes in sealing force which accompany temperature changes show that simple stress against temperature relations are inadequate to describe actual sealing force changes. Also, the direction of applied stress during elastomer moulding produces memory effects in the seal which can remain throughout service and influence properties such as gas-induced rupture by explosive decompression.

1 INTRODUCTION The satisfactory long term performance of elastomer-based sealing elements is important in many industries, particularly where they have a critical safety function. One such industry is the offshore oil and gas business, where premature failure of an elastomeric sealing component can be costly and hazardous, both to life and the environment. In order to reduce unexpected failures even with oil-resistant types of elastomer it is desirable to be able to predict an expected service life of elastomers in their sealing environments. This is often approached by using short term ageing tests that address elastomer compatibility with the service environment by simple immersion testing and measurement of retained mechanical properties. However, many elastomer components 153

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used offshore, especially seals, operate under a combination of applied stress and severe thermal and chemical conditions common when drilling for and producing oil and gas. It is the effect of this combination of factors which has been subjected to the preliminary evaluation described in this chapter. The subjects covered include: comparison of changes in selected properties of stressed and unstressed, filled fluorocarbon elastomer (FKM) exposed to a hot chemically reactive liquid; the effect of temperature excursions on actual sealing force of O-rings; and the possibility that stresses produced whilst moulding a seal can result in memory effects that influence properties such as gas-induced fracture by explosive decompression. In pneumatic tyres, ozone cracking is a long established phenomenon requiring appropriate antidegradant systems in the elastomer formulation to protect against it. The ozone cracking (Braden & Gent, 1961) involves tensile stresses as well as chemical attack of environmental stress cracking. Additionally, for many years evidence has existed that tensile stress increases the amount of liquid that an elastomer can absorb (Treloar, 1970), whilst compressive stresses cause the reverse effect. By inference this should mean that any chemical ageing effects brought about by a hostile absorbed liquid should also increase in the tensile stressed state, for two reasons – more liquid is absorbed, and a stressed region is probably associated with a higher chemical potential than an unstressed. With O-ring seals, although the main mode of deformation applied when loading them into their housing is compressive (their section diameter being greater than the housing groove height), significant tensile strains (up to 25% or more) can exist at certain points. This especially applies to local regions of the surface rubber of the O-ring as follows: • that pressed into the so-called extrusion gap – the joint being sealed between two close metal surfaces – by a combination of the compressive force and the hydrostatic action of the pressurised fluid being sealed; • the region in that adjacent corner of the housing section not directly contacting the fluid; • as a material response to the above deformations, the ring section tends towards a rectangle shape – hence the remaining ‘corners’ also are associated with high tensile stresses, and they contact the pressurised fluid. Preliminary experiments were therefore undertaken to discover something of how stresses and associated strains affect rates of chemical ageing of elastomers in hostile liquids relevant to the offshore oil and gas industry. Tensile and liquid absorption measurements have been made (the latter using O-ring samples). The work described in this chapter is directed towards establishing life prediction methods for elastomeric seals. The preliminary experiments were performed to investigate an approach for life assessment of materials.

2 PRELIMINARY EXPERIMENTS TO STUDY INTERACTIVE EFFECTS OF STRESS AND FLUID ENVIRONMENT Regarding the choice of fluid, it is known that certain corrosion inhibitors (mostly containing amines) have a deleterious effect on some elastomer compounds and can compromise their sealing ability. Although concentration levels are often low in service (at the parts per million level) there is usually a continuous supply so that the effect does not

Stress-Induced Phenomena in Elastomers

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Fig 1. Arrangement of O-rings on spigot to apply strain.

diminish through depletion. Studies at MERL (unpublished) have suggested that different mechanisms may apply for different elastomer/inhibitor combinations, including ionic and free radical attack, as appropriate for the background solvent carrying the inhibitor. For the current work a simple amine (ethylene diamine) was chosen as the chemically active species to simulate the action of commercial inhibitors. The ethylene diamine was used in solution at the relatively high concentration level of 1% to as to produce ageing at rates higher than those usually met in service. It was thought that removal of hydrogen fluoride (HF) by this amine might lead to some extra crosslinking in the FKM. A commercial Viton copolymer (filled FKM) was used for the majority of testing and was designated FKM#1. The material is often used for sealing at high temperatures in the presence of diverse petroleum-related fluids. (One test was performed on a second FKM (#2) thought to be similar to the first, but from a second supplier, and on a third FKM (#3) cured with a different oxide system – see below.) Using reflux glassware apparatus, liquid absorption (mass uptake) measurements at 50oC, 75oC and 100 oC were performed on O-rings conforming to BS 1806 (1989) size 312 [1’’ (25mm) outside diameter, 0.210’’ (5.3mm) section]. It was easier to apply fixed strains rather than fixed stresses to the O-rings: compressive strains of 0%, 11% and 20% were applied. Unstrained O-rings were allowed to lie freely in the 1% amine aqueous solution, whereas the strained O-rings were located on special two-seal piston (spigot) mode arrangements as shown schematically in Figure 1: in this arrangement, liquid contacts only the “outer” surface of each O-ring. The strained O-rings were removed for each weighing, and then replaced in the same location.

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Elastomers and Components: Service Life Prediction – Progress and Challenges Strain level

12.5

0% 11% 20%

10 7.5

100°C

m (%) 5 2.5 0

75°C 50°C 0

1

2

3 t1/2 (days1/2)

4

5

Fig 2. FKM#1 mass uptake (m) of O-rings in 1% ethylene diamine solution.

Fig 3. Mass uptake (m) of 100% water at 155°C by typical FKM copolymers.

Figure 2 shows the FKM data obtained thus far for these weighings, in the usual form of plots of % mass uptake versus the square root of exposure time. As would be expected, uptake has increased more rapidly at higher temperatures. However, equilibrium values have not been achieved. Moreover, the plots do not take the classical form of initial linearity (with positive gradient), leading to a horizontal region at equilibrium absorption. Instead, the plots demonstrate an upturn after 10-20 days, so that exposures are still continuing at the time of writing. This upturn was particularly pronounced at 100oC. A likely explanation arises from another mass uptake test using the same sized O-rings, using


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σ (MPa)

γ (%) Fig 4. Typical stress (σ) against strain (γ) plot for unaged FKM#1 (Incremental modulus IM (MPa) [5-25%] = gradient (y/x) of line between γ = 5 and 25 %).

FKM#2 and FKM#3. These experiments were performed at 155oC in water (without corrosion inhibitor) within a pressure vessel. Results are plotted in Figure 3. FKM#2 exhibits a significant upturn, of the type just discussed: at the same time, it was observed that the elastomer began showing signs of degradation, in the form of blistering and splitting. The mechanism is thought (Revolta, 1986) to involve the particular oxide/hydroxide cure system employed (MgO, Ca(OH)2) – in contrast, if a lead oxide system is used (FKM#3), the upturn does not occur. Hence the results in Figure 2 suggest that this degradation phenomenon can occur for an FKM at lower temperatures in the presence of amine. Figure 2 shows a major difference between the uptake for an unstrained O-ring of FKM#1 and an O-ring of the same material at 11% compression. However, the unstrained O-rings were completely exposed to test liquid whereas, with the 11% and 20% O-rings, only outer faces contacted the liquid. Hence the small differences between 11% and 20% strained results are more significant than the larger differences between 0% and 11%. The dominance of the degradation upturn precludes further assessment. Turning to mechanical properties, tensile samples (Type 2 according to BS 903 Part A2 1989) of FKM#1 were exposed to the 1% ethylene diamine solution at 50, 75 and 100°C for up to 24 days. The samples were immersed both free standing and strained (20%) in simple apparatuses made for the purpose: in this case, the apparatuses did not significantly affect the exposed surface areas. A strain of 20% was used as this level can be experienced in seals in high pressure applications at and around any areas of extrusion. Plots of engineering stress against strain were obtained at room temperature and at a cross-head speed of 500 mm/minute after each exposure condition. Following the tensile test, the sample was

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IM (MPa)

t (days) Fig 5. Change in incremental modulus (IM) of strained and unstrained FKM#1 tensile samples exposed at various temperatures and exposure times (t).

0.6 Crosslinking 0.4 0.2 R

0

0

25

50

75

100

q (°C) 125

– 0.2 – 0.4

strained Degradation

– 0.6 unstrained – 0.8 Fig 6. Effect of stress on balance of ageing mechanism when applied to a set strain during FKM#1 exposures at temperature (θ). (R is rate of modulus change in MPa per day.)


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discarded. Because initial moduli were high, no differences could be perceived here for the standard elastomer extensometer used. An incremental modulus (from 5 to 25% strain) was therefore calculated for each condition as indicated in Figure 4 which shows a typical tensile stress-strain curve for unaged FKM#1. The moduli for FKM#1 from all six combinations of prestrain and temperature are plotted in Figure 5 against exposure time. Although both positive and negative slopes are observed, clearly the effect of the prestrain during ageing has been to increase the modulus compared to the unstrained situation. These data can be summarized by plotting the rate of modulus change against the exposure temperature, for both unstrained and the strained condition (Figure 6). The difference arising from the application of a 20% prestrain shows clearly here and can be interpreted as follows. Competing reactions of amine-induced crosslinking and amine-enhanced degradation can occur in FKM. At higher temperatures degradation reactions dominate while at lower temperatures crosslinking dominates – an effect enhanced by applied strain. In the tests on unstrained testpieces, degradation reactions dominated for all temperatures and other conditions. For temperatures above 100°C degradation reactions dominated both for prestrained and unstrained testpieces. Conventional test procedures for assessing the interaction of elastomers and liquids – American or British Standards (ASTM or BS) for example – involve the use of simple unstrained testpieces. The results reported here indicate that such conventional tests may not reveal the complete picture. Application of realistic stresses and strains to samples during immersion testing can lead to reduced life expectations. This can have considerable impact on safety and environmental issues where predictable performance must be guaranteed.

3 TRANSIENT EFFECTS OF TEMPERATURE ON SEALING FORCE A compressed elastomeric seal will lose sealing force when the temperature is reduced due to thermal contraction and thermodynamic effects. It has been shown experimentally that this loss in force is likely to be substantially greater in practice than would be predicted theoretically. For a seal which had been in place for two months at 80 oC, a drop in temperature to 23oC will theoretically reduce the sealing force by 27%. Experimental measurements show that the actual drop in force was 50%. This is an important consideration in seal design. Reasons for the higher measured drop are explained below. 3.1 THE EFFECT OF TEMPERATURE REDUCTION ON SEALING FORCE

Many seals have to accept changes in temperature during service. It is a commonplace observation that, when leakage occurs, it is often after a reduction in temperature, although the leak may not be observed until the temperature is once again raised. Taking the example of a simple O-ring seal, two factors reduce the sealing force when the temperature is lowered. The first concerns thermal contraction of the seal, and the second is a thermodynamic effect whereby the stress in a strained elastomer is proportional to absolute temperature (Treloar, 1970, 1975). When we consider that a compressed seal is losing sealing force because of stress relaxation from the moment of its installation, it is easy to appreciate that a further reduction in sealing force, due to a temperature drop, may lead to leakage.

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3.1.1 THERMAL CONTRACTION

The coefficient of linear thermal expansion is typically 2 x 10-4K-1 for an elastomer, whereas the equivalent coefficient for steel (the usual housing material) is 1.2 x 10-5K-1. This means that an elastomeric seal will contract several times more than its housing when the temperature is lowered. Because the stress distribution in an O-ring is complex, and because behaviour is nonlinear, it is not straightforward to calculate the reduction in sealing force which will accompany thermal contraction. To get some idea of the magnitude of the effect, however, we will take the simple example of a 5mm section O-ring compressed by 20% to form a seal, i.e. compressed by 1mm. A temperature drop from 150oC to ambient (say 20oC) will lead to a reduction in size of 0.1mm, i.e. 10% of the initial strain. We could determine the resulting reduction in sealing force either by use of finite element methods, or, more simply, by reference to the experimentally measured stress/strain curve of the seal in its housing. This would give us the theoretically expected reduction in sealing force due to the temperature drop. We will see below that this calculation will underestimate the reduction in force which actually occurs. 3.1.2 THERMODYNAMIC FORCE REDUCTION

The statistical theory of rubber elasticity predicts that the stress in a strained elastomer is proportional to absolute temperature. A related phenomenon can easily be demonstrated by hanging a weight on a strip of unfilled rubber such as that used for elastic bands. If the strip is heated using a hot air blower, the weight will rise, i.e. contrary to expectations, the strip will get shorter, and this is known as the Gough-Joule effect. For a relatively simple description of this and related phenomena see Treloar (1970 or 1975). Taking the O-ring example above, we can calculate the reduction in stress which will theoretically accompany a reduction in temperature from 150oC (423K) to 20oC (293K). This is a reduction in temperature of 130K. According to the statistical theory of rubber elasticity, a 31% reduction in absolute temperature will result in a 31% reduction in sealing stress. This reduction in stress will be added to the reduction resulting from thermal contraction of the seal, so it is easily seen that the sum of the effects is certainly not negligible for seals which can experience a significant temperature drop in service. 3.2 EXPERIMENTAL RESULTS

A number of tests have been carried out to validate the above conclusions. These are described in more detail elsewhere (Derham, 1997) and will be described only in broad outline here. In order to eliminate complications from physical stress relaxation effects, which have their highest rate in the early stages after compression of a seal, temperature cycling tests were carried out on seals which had already been compressed for at least two months. Tests have been carried out both on a nitrile (NBR) and on a fluorocarbon elastomer (FKM), Viton E60C® (see Figure 7) with essentially similar results. For the FKM elastomer, an O-ring of 0.210” (5.3mm) section and 1” (25mm) outer diameter which had been compressed for two months at 80oC, was subjected to temperature cycling between 80oC and ambient (23oC) with in-situ sealing force measurement as described by Derham (1997). Taking account of both thermal contraction and the thermodynamic effect, it was calculated that the sealing force should theoretically fall by 27% when the temperature was reduced, and, of course, rise by 27% when the temperature was again


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Fig 7. Relaxation results for FKM elastomer O-rings showing (a) initial two month relaxation at 80°C and (b) subsequent temperature cycling (80ºC to 23ºC) tests continued immediately from end of (a).

raised. The change in sealing force measured experimentally was essentially reversible as expected but was 50%, nearly double that predicted theoretically. The explanation for why the actual drop in sealing force is so much greater than that predicted theoretically is believed to be associated with compression set. Put simply, an O-ring which has suffered compression set will have stiffer force/deformation characteristics than a new O-ring. Therefore a small change in deformation, brought about by contraction due to a temperature drop, will have a proportionately larger effect on the force in an O-ring which has

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Fig 8. Fracture due to explosive decompression in sheet cut across the direction of flow – “cross flow”.

Fig 9. Explosive decompression fracture in sheet cut with the flow – “with flow”.

been compressed for some time, than it will have on an otherwise identical new O-ring. In effect, the ‘shape factor’ of the seal has increased due to compression set, shape factor being the loaded area over which stress is applied divided by the force-free area. Unfortunately, no simple method has yet been devised for predicting the actual drop in sealing force for a ring which has been in place for some time. The force/deformation characteristic will be dependent on the exact shape of the seal housing, so that it will be


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different for different sealing configurations even if the seals are identical. Tests using the actual housing conditions are therefore necessary for evaluation of the effect, and are essential for critical applications. However, it has been shown (Derham, 1997) that the effect of compression set on force/deformation behaviour can be detected quite early on. Thus screening of candidate materials may be possible over quite short timescales. The behaviour of a nitrile O-ring (56 mm inner diameter, 6.8 mm cross-sectional diameter) demonstrates the point. The seal was compressed between flat platens by 20% at 23 o C. The incremental stiffness (at 20% compression) was found to increase by 18% after only 15 hours. Thus some measure of the effect described here can be made quite quickly in order to compare candidate materials for an application.

4 STRESS EFFECTS IN GAS-INDUCED RUPTURE IN ELASTOMERS Oilfield production can involve gas pressures and temperatures up to approximately 100MPa (15000psi) and 200oC respectively. Rapid loss of pressure can cause rupture of elastomeric seals being used to contain the fluids. This phenomenon, commonly termed explosive decompression, has been discussed in some detail (Campion, 1990; Briscoe et al, 1994; Stevenson & Morgan, 1995), but is not yet quantified or fully controlled. A particular stress-related aspect has been examined. 4.1 EFFECTS OF MEMORY OF ELASTOMER PROCESSING

It has been observed that in flat elastomeric sheets explosive decompression frequently manifests itself as two-dimensional fractures along the central plane. This prompted an examination of the effect which rubber flow during moulding has on explosive decompression damage. A suitable ‘semi-plunger’ mould with side slots which allowed excessive lateral flow was employed to give a deep sample of nitrile rubber: a high moulding pressure was used. After curing, a thin sheet which crossed the direction of flow was obtained by cutting vertically through the sample with a lubricated mechanical rotary slicer (“cross-flow” sheet). A “with flow” sheet was also cut in the direction of flow, a more normal situation, so that comparisons could be made. The sheets were then immersed in methane (at 100oC and 17MPa) for three days to allow diffusion equilibrium to be established. The pressure was then rapidly released. On subsequent examination, the “cross-flow” sheet showed few fractures (splits) compared with the “with-flow” sheet. The splits traversed the “cross-flow” sheet (Figure 8) but ran along the “with-flow” sheet (Figure 9) in such a manner to indicate that in both cases they derived from original interfaces between stacked layers of uncured materials. Even if processinginduced coalescence of these layers had largely been completed, oriented stress regions presumably remained, to give “memory lines or surfaces”. Hence the direction of flow can be a major factor in the form of fractures obtained. Regarding O-ring seals, a common means of manufacture can include a specialized preforming extrusion stage. Figure 10 shows a section of an O-ring after explosive decompression testing: the central splits could well have arisen as a consequence of memory effects of the types described above. Also present in the left-hand bottom region of the seal (extrusion area) are a number of subsidiary splits concentrated at what constitutes a relatively high-strain “corner” of the deformed seal during service.

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Fig 10. O-ring section showing explosive decompression fractures after tests in realistic housing.

5 CONCLUSIONS Three areas where stresses and associated strains can affect properties involved in elastomeric sealing of pressurised fluids have been studied. The rather complex situation involving competing reactions of crosslinking and degradation for a typical FKM in amine solution has shown that using simple unstrained testpieces following conventional standard practice may result in underestimation of service life compared to assessment using realistic stress and strain. Theoretical calculations of sealing force reduction accompanying temperature decreases can underestimate the reduction in force which actually occurs and which may result in leakage. This occurs because the shape factor of a seal will increase due to compression set. And finally, memory features induced during flow in the elastomer moulding process can influence the appearance of splits caused by explosive gas decompression events.

REFERENCES Braden M & Gent AN (1961) “The attack of ozone on stretched rubber vulcanisates. The rate of cut growth & Part 2 Conditions for cut growth” J Appl Polym Sci, 3, 90-99 & 100-106. Briscoe BJ, Savvas T & Kelly CT (1994) “Explosive decompression failure of rubbers: a review of the origins of pneumatic stress induced rupture in elastomers”, Rubber Chem Technol 67 (3), 384-416. BS1806 (1989) Specification for dimensions of toroidal sealing rings and their housings. Campion RP (1990) Cellular Polymers, 9 (3), 206-228. Derham CJ (1997) “Transient effects influencing sealing force in elastomeric o-ring seals”, Plastics, Rubber and Composites Processing and Applications, 26 (3), 129-136. Revolta WNK (1986), DuPont Dow Elastomers Ltd (UK), personal communication. Stevenson A & Morgan GJ (1995) “Fracture of elastomers by gas decompression” Rubber Chem Technol, 68 (2), 197-211. Treloar LRG (1970) Introduction to Polymer Science, Wykeham Publications, London. Treloar LRG (1975) The Physics of Rubber Elasticity, 3rd edition, Clarendon Press, Oxford.

CHAPTER 11

Magnetorheological Devices M Lokander and B Stenberg Department of Fibre and Polymer Technology, KTH Stockholm, Sweden

SYNOPSIS The mechanical properties of magnetorheological materials can be changed and controlled by an applied magnetic field. This makes the group of materials interesting for damping applications and vibration control. Most of the work done so far has been performed on magnetorheological fluids, which are suspensions of magnetically polarizable particles in a carrier liquid. For some applications it would be preferable to use a rubber or a gel instead of the liquid. Such magnetorheological solids would not have any problems of sedimentation of particles, the devices could be made smaller and cheaper since there would be no need of a container for the fluid, and the changes in the mechanical properties could be expected to be faster than in a liquid. However, magnetorheological solids work only in the pre-yield region while the fluids typically work in the post-yield region, so the two groups of materials are therefore more complementary than competitive. Examples of rubbers that are interesting for magnetorheological applications are silicone, natural rubber and nitrile rubber. The addition of iron particles to the rubber will influence the service life of these rubber devices. For optimal function of the devices, prediction of service life is necessary. Such predictions are also necessary for magnetorheological devices to become commercially successful.

1 BACKGROUND The idea of changing the mechanical properties by applied fields is not new. In the late 19th century it was observed that an electric field applied across a mixture of glycerin, paraffin and castor oil caused a small and reversible change in viscosity. Winslow discovered a similar but larger effect, using powdered oil dispersions and introduced the term electrorheology (ER) in 1949 (Weiss & Carlson, 1993). At the same time Rabinow discovered a similar effect by applied magnetic fields, magnetorheology (MR). During the 1950s many patents based on these phenomena, especially MR, were published, but none became commercial. Since the difficulties were larger than expected, the interest for ER 165

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and MR decreased. In the 1980s though, with new faster generations of computers, new applications were made possible and again the field of ER and MR seemed interesting (Jolly et al, 1999). The renewed interest was mainly focused on electrorheological fluids (ERF). At this time ERF were thought to be the ones that would be easiest to make commercial applications from. This was because the particles in magnetorheological fluids (MRF) were larger and heavier and therefore sedimentation was a huge problem. MRF have also a natural limitation in strength in the saturation magnetization of the particles in the fluid, therefore it was long believed that ERF with larger effect than MRF would be developed. Further magnetism, as a more abstract phenomenon, was also thought to be more difficult to use (Filisko, 1996). Still the strength of MRF are some order of magnitude greater than that of ERF (Wiess et al, 1994), and it is much easier to achieve the required fields for MRF than for ERF. Because of this a growing part of the interest is focused on MR. There are a few commercial applications using MRF but none using ERF (Jolly et al, 1999). The Department of Polymer Technology at KTH have been working with ER and MR since 1994 and have presented work at the 6th and the 8th international conferences on electrorheological fluids, magneto-rheological suspensions (Nordberg et al, 1997; Lokander & Stenberg, 2001). Much of the work is summerised by Lokander (2004).

2 MR- AND ER-FLUIDS ERF and MRF are suspensions of polarizable particles in a carrier fluid. When an electric or magnetic field is applied, the particles polarize and align with the field. The interparticle forces cause the particles to form chains that results in a reversible increase in apparent viscosity by several orders of magnitude. When the field is removed the fluid immediately returns to its original state. Both the activation and the deactivation of the fluids are completed within milliseconds after the field is turned on or off (Weiss & Carlson, 1993; Jolly et al, 1999). Although there is an increase in apparent viscosity from a macroscopic point of view, the actual plastic viscosity, defined as the change in stress per unit change in shear strain, is approximately constant as the field is varied. The fluids in the absence of the field behave approximately as Newtonian fluids. When the field is applied the behaviour is as Bingham bodies (Weiss & Carlson, 1993; Jolly et al, 1999). The yield stress (τ y) of the Bingham bodies, which is field dependent, is the most important property of MRF as well as of ERF. The required magnetic field for activating MRF is in the order of magnitude of tenths of Tesla (Jolly et al, 1999, which may be achieved using an ordinary 12V battery and a proper magnetic circuit). The corresponding electric field for ERF is in the order of magnitude of kV, which makes it necessary to use high voltage equipment (Weiss & Carlson, 1993). The possible applications for ER- or MR-materials are numerous. For example clutches, brakes, dampers and shock absorbers have been suggested for both ER- and MR-fluids (Weiss & Carlson, 1993; Jolly et al, 1999). Commercial products today are a seat damper for heavy vehicles and a compact smooth acting brake for exercise bikes, both using MR-fluids. Both products are sold by Lord Corporation. Lord is also the only commercial supplier of MR-fluids today (www.mrfluid.com).

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3 MR-SOLIDS There are some drawbacks with the use of fluids. There is a need for a container to keep the fluid in place. Further there is always the sedimentation and agglomeration problem. Even though there are some fluids that are called “non-sedimenting” or “stable”, the properties may not be constant when stored for long periods of time. These “stable” fluids have very high zero-field viscosity, which is also a problem. When in use the fluids show an increase in modulus after some 100 000 cycles of mechanical deformation. This “in use thickening” is a newly recognized problem with MR-fluids (Carlson, 2001). All these drawbacks would be avoided if the matrix were a soft solid material, like a rubber or a gel, instead of a liquid. In such MR-solids the magnetic field would cause an increase in the shear modulus. The MR-effect of such MR-solids would be quite small since the modulus is relatively high even without the applied field (Ginder et al, 1999). However the response is larger than you would expect from the data of the fluids (Brostow, 2001). The response can be expected to be faster since the particles are fixed, but this is probably of little importance since the response is very fast in fluids as well (Ginder et al, 1999). MR-solids can be manufactured by simply mixing magnetically polarizable particles into an unvulcanized rubber. If a magnetic field is applied during the vulcanization, the particles tend to form chains within the rubber, which increase the MR-effect (Ginder et al, 1999). Another possibility is to mix the particles into a gel instead of a rubber (Shiga et al, 1995). There are no commercial devices using MR-solids yet, but a variable stiffness bushing for reducing brake shudder in automotive have been patented by Ford (Stewart et al, 1998).

4 PROPERTIES OF MR-RUBBERS The MR-effect (increase in modulus caused by a magnetic field) of a MR-rubber depends mainly on the type of particles used. The only influence of the matrix material is that a softer material may give a larger relative increase in modulus. The interaction between the particles and the matrix may be important, but more work has to be performed on that issue to be able to draw conclusions. The most important properties of the particles are the saturation magnetization, the remnance, the size and the shape. The MR-effect is limited by the saturation magnetization of the particles (Ginder & Davis, 1994). If the particles are remnant some magnetic forces will still be present after the removal of the applied magnetic field, which means that the original modulus is not achieved unless a field in the opposite direction is applied. The MR-effect of MR-fluids increases with increased particle size (Kordonski et al, 1997). Therefore the use of larger particles is interesting in rubbers, where sedimentation is no problem. The shape may also influence the MR-effect in rubbers due to rotation of the particles or the demagnetizing field. The most commonly used particle type, both in fluids and solids, is carbonyl iron which is micron sized spherical particles of very pure iron (Jolly et al, 1999 & 1996; Ginder et al, 1999). Pure iron is characterized by high magnetic saturation and low remnance, and is thereby suitable for MR-materials. Particle sizes in the micrometer range are optimal for the fluids, but for MR-solids even larger particles (50-100 µm) may be used (Kari et al, 2002; Lokander & Stenberg, 2003(a & b); Shiga et al, 1995). Matrix materials for MR-rubbers have been natural rubber (Ginder et al, 1999), silicone

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(Jolly et al, 1996) or nitrile rubber (Lokander & Stenberg, 2003(a & b)). Theoretically any matrix material could be used, as long as the modulus is not too high. The maximum MR-effect reported is 50% increase in modulus, at a magnetic field of 1T (Nichols et al, 1999). The material in this case was natural rubber with carbonyl iron particles that had been aligned within the material before the curing. However, in another investigation, materials with larger irregularly shaped pure iron particles showed a greater MR-effect than similar material with carbonyl iron (Lokander & Stenberg, 2003a). The particles had in this case not been aligned before the curing and the measurement was performed at a relatively low field strength (0.2T). This larger effect was explained by the fact the critical particle volume concentration, the concentration where the distance of the particles are at minimum, of the particles was close to the actual concentration of the materials. If it is not possible to decrease the distance between the particles by use of a magnetic field before the curing, the critical concentration of the particles used will be close to 30% by volume. The highest MR-effect is obtained at an iron particle content of about 30% by volume (Lokander & Stenberg, 2003(a & b); Kordonski et al, 1997; Davis, 1999). Fortunately the mechanical properties do not deteriorate very much until even higher contents are used, i.e. above the critical concentration level (Lokander & Stenberg, 2003a).

5 SERVICE LIFE MR-rubbers have a long way to go before commercial products are on the market. There are several items that have to be investigated before that, such as maximizing the effect at any given strain amplitude, the high frequency behaviour etc. One area, where almost no work has been done until recently is the long-term properties of the materials. The iron particles are, from a rubber materials point of view, non-reinforcing fillers. Incorporation of non-reinforcing fillers in a rubber compound will increase the creep and relaxation rates (Andrews, 1963; Derham, 1973). The particles may induce crack growth, which will decrease the fatigue life of the materials (Andrews, 1963). Considering the large amounts of iron needed to obtain a substantial magnetorheological effect, these aspects are very important for magnetorheological rubber materials (Poh et al, 2002). Furthermore, the incorporation of iron particles will influence the oxidative degradation of the materials. The particles are generally oxidised at their surface, which results in incorporation of large amounts of oxygen into the bulk of the material. The need to predict the long-term properties and service life of devices using this new group of materials is obvious. Otherwise surprises like the “in use thickening” of MRfluids (Carlson, 2001) may show when the devices have been used for a while.

REFERENCES Andrews EH (1963) “Reinforcement of rubber by fillers” Rubber Chem Technol, 36, 325-336. Brostow W (2001) Performance of Plastics Hanser Publishers, Munich. Carlson JD (2001) “What makes a good MR fluid?” 8th Int. Conf. Electro-rheological (ER) Fluids and Magneto-rheological (MR) Suspensions, Nice, France, 9-11 July.

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Davis LC (1999) “Model of magnetorheological elastomers” J Appl Phys, 85(6), 3348-3351. Derham CJ (1973) “Creep and stress relaxation of rubbers – the effects of stress history and temperature changes” J Mater Sci, 8, 1023-1029. Filisko FE (1996) ER V: “The present and the future” Int J Mod Phys B, 10, 23-24. Ginder JM & Davis LC (1994) “Shear stresses in magnetorheological fluids: Role of magnetic saturation” Appl Phys Lett, 65(26), 3410-3412. Ginder JM, Nichols ME, Elie LD & Tardiff JL (1999) “Magnetorheological elastomers: Properties and applications” SPIE, 3675, 131-138. Jolly MR, Carlson JD, Muñoz BC & Bullions TA (1996) “The magnetoviscoelastic response of elastomer composites consisting of ferrous particles embedded in a polymer matrix” J Intel Mater Syst Struct, 7, 613-622. Jolly MR, Bender JW & Carlson JD (1999) “Properties and applications of commercial magnetorheological fluids” J Intel Mater Syst Struct, 10, 5-13. Kari L, Lokander M & Stenberg B (2002) “Structure-borne sound properties of isotropic magnetorheological rubber” Kautschuk Gummi Kunststoffe, 55(12), 1-5. Kordonski WI, Gorodkin SR & Novikova Z A (1997) “The influence of ferroparticle concentration and size on MR fluid properties” 6th Int Conf Electro-rheological Fluids, Magneto-rheological Suspensions and their Applications, Yonezawa, Japan, 22-25 July. Lokander M (2004) “Performance of magnetorheological rubber materials” PhD Thesis, Royal Institute of Technology (KTH), Stockholm. Lokander M & Stenberg B (2001) “Isotropic magnetorheological nitrile rubbers with large iron particles” 8 th Int Conf Electrorheological (ER) Fluids and Magneto-rheological (MR) Suspensions, Nice, France. Lokander M & Stenberg B (2003a) “Performance of magnetorheological rubber materials” Polymer Testing, 22(3), 245-251. Lokander M & Stenberg B (2003b) “Improving the magnetorheological effect in isotropic magnetorheological rubber materials” Polymer Testing, 22(6), 677-680. Nichols ME, Ginder JM, Tardiff JL & Elie LD (1999) “The dynamic mechanical behaviour of magnetorheological elastomers” Meeting of Rubber Division, American Chemical Society, Orlando, Florida, September, 21-24. Nordberg P, Stenberg B, Lizell M & Asplund J (1997) “An electrorheological mount with fixed radial valve” 6th Int Conf Electro-rheological Fluids, Magneto-rheological Suspensions and their Applications, Yonezawa, Japan, 22 -25 July. Poh BT, Ismail H & Tan KS (2002) “Effect of filler loading on tensile and tear properties of SMR L/ENR 25 and SMR L/SBR blends cured via semi efficient vulcanization system” Polymer Testing, 21, 801-806. Shiga T, Okada A & Kurauchi, T (1995) “Magnetoviscoelastic behaviour of composite gels” J Appl Polym Sci, 58, 787-792. Stewart WM, Ginder JM, Elie LD & Nichols ME (1998) US Patent 5,816,587. Weiss KD & Carlson JD (1993) “Material aspects of electrorheological systems” J Intel Mater Syst Struct, 4, 13-34. Weiss KD, Carlson J D & Nixon DA (1994) “Viscoelastic properties of magneto- and electrorheological fluids” J Intel Mater Syst Struct, 5, 772-775. www.mrfluid.com

CHAPTER 12

Selection of Elastomers for a Synthetic Heart Valve S Baxter, JJC Busfield and T Peijs Department of Materials Queen Mary, University of London

SYNOPSIS The advent of the polymeric synthetic heart valve will hopefully allow the limitations of other commonly used artificial heart valves to be overcome. Currently the valves adopted in practice include mechanical heart valves and biological heart valves. The mechanical valves are prone to thrombosis formation in the blood and require long-term anticoagulant therapy. The biological valves lose their tissue replacement function as a result of their chemical treatment which results in tissue fatigue damage in service. Polymeric synthetic heart valves that mimic the function of a real valve will hopefully overcome these difficulties. In this chapter, various elastomeric materials (polyurethane, silicone rubber and EPDM), that can be used to make polymeric synthetic heart valves, have been assessed by measuring their strain energy release rate for a wide range of crack growth rates. This was measured using static loading under a variety of conditions in order to evaluate their potential performance as target materials. Polyurethane is the most suitable matrix material of the three candidates from a consideration of the tear resistance. The behaviour of the polyurethane is similar to that of a strain crystallising material and as a result it would appear that some comparable form of reinforcement takes place. At the temperatures encountered in the body there is a significant decrease in the tearing energy for a given crack growth rate due to a reduction in the viscoelasticity. Despite this, it would still appear that polyurethane is the most suitable material for use in a synthetic heart valve.

1 INTRODUCTION Surgeons currently use a wide range of artificial heart valves to replace natural heart valves that become damaged through disease or problems such as calicification (deposition of calcium ions on the natural valve that inhibit its function) and thrombosis (clotting induced by damage to red blood cells that flow through the natural valve). Replacement artificial valves still have their drawbacks, mechanical valves are prone to thrombosis formation (De 171

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Fig. 1 (a) Composite-like structure of the aortic heart valve leaflet and (b) a prototype EPDM/Polyethylene synthetic composite heart valve.

Wall et al, 2000) and require the use of anticoagulent therapy and biological valves are prone to tissue degradation (Piwnica & Westaby, 1995) that leads to fatigue failure. In response to these problems synthetic heart valves, which mimic natural valve behaviour, have been developed (Herold et al, 1987), however during in vitro testing the valves are prone to fatigue failure due to calcification in regions of high stress concentrations because of high flexion (Hilbert et al, 1987). Recently, a synthetic heart valve has been developed encompassing the composite structure of the natural valve incorporating an elastomeric matrix with a polymeric fibre (Cacciola, 1998) both are illustrated in Figure 1. Materials selection of an appropriate fibre and matrix can be based upon several characteristics, the foremost being biocompatibility. This chapter is mainly concerned with selecting a candidate elastomeric matrix material, based upon the measurement of their crack growth resistance. The tearing behaviour of elastomers was initially examined by Rivlin & Thomas (1953), based upon crack growth being determined by the elastic strain energy released on the tearing to create two new fracture surfaces. Tearing energy T, can be defined as:

(1) where c is the length of the crack in the specimen, h is the thickness and U is the total elastic strain energy stored. The subscript l indicates that the external boundaries do not move and hence no work is done on the test piece, as the crack extends. The tearing energy versus crack growth rate relationship is an intrinsic material property that is independent of the test piece geometry (Rivlin & Thomas, 1952). Figure 2 shows graphically the relationship that is established mainly for many non

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Fig. 2 Schematic of the tearing energy (T) and crack growth rate (r) relationship for a non-crystallising elastomer.

strain crystallising elastomers tested using a pure shear geometry. The graph has three distinct regions (Tsunoda et al, 2000) and in each the crack propagation behaviour is different. In region A the crack growth is slow and the fracture surface is rough. In region B, which is known as the stick-slip region the crack growth continuously varies between slow and fast tearing rates. In region C the tearing is faster with a more uniform rate and smoother fracture surfaces.

2 EXPERIMENTAL METHODS Three elastomers [EPDM (ethylene propylene diene monomer), silicone and PU (polyurethane)] were initially targeted due to their possible bio-compatibility. Each of these materials was evaluated as candidate materials for the matrix of the synthetic composite heart valve using crack growth rate measurements. The elastomers were all produced using solution casting; dibenzoyl peroxide was used as a curing agent, 1% and 3% by mass for EPDM and silicone respectively, both dissolved in Xylene. Vulcanisation conditions for these two elastomers were 120oC for four hours. PU was dissolved in Dimethylformamide (DMF) which was cast and then heated in an oven at 100oC for one hour to allow the DMF to evaporate and the PU to form. The two simple test piece geometries ‘trouser’ and ‘pure shear’, which are shown in Figure 3, were used to measure the static crack growth rate versus tearing energy behaviour of the three materials. The test sheet thickness for all the samples evaluated in this work were approximately 0.2mm. The dimensions of the pure shear test piece were 175mm width by 20mm height. A

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Fig. 3 a) trouser and b) the pure shear test piece geometries; where T = tearing energy; W = strain energy density; F = applied force; h = speciment thickness; λ = extension ratio; w = leg width; lo = original height.

pre-crack of 40mm was cut with a razor blade to ensure that the complications caused by edge effects were avoided. The tearing energy, T = loW for a given fixed applied strain was calculated using measurements for the strain energy density, W, which was in turn calculated from the area under a stress versus strain curve for an un-cracked specimen extended to the same strain. The crack growth rate for each fixed applied strain was determined using a video camera monitoring the average crack profile length with time. The dimensions of the trouser test piece were 30mm width and 50mm length with a precrack of 25mm cut with a razor blade. The trouser tests were carried out at various constant cross- head speeds, and hence crack growth rates using a screwdriven Instron 1122. The tearing energy T=2Fλ/h-wW, was calculated from a measure of the peak force, F at a constant cross-head displacement, in each leg during tearing, the extension measured in the trouser leg at the onset of tear, λ, and the strain energy density, W. The strain energy was again measured using the area under the stress versus strain graph for uncut test samples tested to the same strain. The average crack growth rate was taken directly from a measurement of the crosshead speed divided by 2λ. Testing was carried out at both room temperature and at body temperature (37°C).

3 RESULTS AND DISCUSSION In Figure 4, it is clear that for all three materials the relationship between the crack growth rate and the tearing energy are broadly consistent for each material irrespective of the specific test piece geometry adopted confirming the work of several other researchers (Ahagon & Gent, 1975; Bhowmick et al, 1983; Kumudine & Mark, 1999). This validates the tearing energy approach as being a suitable method to predict the relationship between the crack growth rate and the externally applied forces. The


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Fig. 4 (a) The relationship between crack growth rate and tearing energy for PU, EPDM and silicone comparing the two test piece geometries and (b) a comparison of the PU elastomer material at room and body temperature.

average crack growth rate for equivalent tearing energies is slightly higher for the trouser tear test piece than the pure shear test piece and this results from some suppression of the stick slip behaviour during the trouser tear test. The strength of the materials can be ranked according to the results with PU being the strongest and the silicone rubber being the weakest. Crack growth is inhibited by the viscoelastic energy being lost during the loading cycle and hence not being available to drive the crack. It is interesting to note that the materials rank according to the extent of the hysteresis behaviour during loading and unloading, with PU having the largest hysteresis (Buist, 1987) and also the highest tear resistance. It is clear that both the

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silicone and the EPDM are not suitable target materials for a synthetic heart valve due to their much lower tear resistance. The PU demonstrates very interesting crack growth behaviour. Below a certain tearing energy of about 100kJm-2 (or log10 5[T/Jm-2]), it appears not to tear exhibit a n y t e a r i n g be h a v i o u r. A bo v e t h i s c r i t i c a l v a l u e t h e c r a c k g r o w t h r a t e f o r polyurethane shows rapid fracture only at rates above 0.01ms -1 as demonstrated in Figure 4. This suggests that something in addition to viscoelastic losses are occurring at the crack tip. Possible mechanisms include plastic yielding of the hard segments within the micro-phase structure of polyurethane, (Darnell et al, 1997) crack tip blunting and possibly strain induced crystallisation, all of which might inhibit crack growth. This type of behaviour is typical for a strain crystallising elastomer such as NR (natural rubber) whereby below a certain high threshold the crack growth behaviour is suppressed in tearing. As the temperature was increased to that of the body at 37oC a significant decrease in the tearing energy required to propagate a crack at a given crack growth rate for the PU was observed (Figure 4b). This phenomenon arises as a result of the decrease in the viscoelastic work done by the elastomer when stretched at the elevated temperature (Tsunoda et al, 2000). The next stage in this work would require the in service fatique crack growth behaviour to be characterised for the specific conditions that are encountered in the prosthetic heart valve design.

4 CONCLUSIONS PU is the most suitable matrix material of the three candidates from a consideration of the tear resistance. The behaviour of the PU is similar to that of a strain crystallising material and as a result it would appear that some comparable form of reinforcement takes place. At the temperatures encountered in the body there is a significant decrease in the tearing energy for a given crack growth rate due to a large reduction in the viscoelastic effects. Despite this it would still appear that PU is the most suitable material for the matrix material used in a composite heart valve.

REFERENCES Ahagon A & Gent AN (1975) J Polym Sci, 13, 1903. Bhowmick AK, Gent AN & Pulford CTR (1983) “Tear strength of elastomers under threshold conditions”, Rubber Chem Technol, 56, 226-232. Buist JM (1987) Developments in Polyurethane, Applied Science Publications. Cacciola G (1998) “Design, simulation and manufacturing of fiber reinforced polymers heart valves” PhD Thesis, Eindhoven University of Technology. Darnell CW, Hung-Joong K & Benson RS (1997) Polymer, 38, 2609. De Wall RA, Qasim N & Carr L (2000) “Evolution of mechanical heart valves” Ann. Thorac. Surg., 69, 1612-1621. Herold M Lo, HB & Reul H (1987) “The Helmholtz Institute trileaflet polyurethane heart valve prosthesis: design, manufacturing and first in vitro and in vivo results”, (p232) Elsevier Science Publishers BV, Amsterdam, 232.


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Hilbert SL, Ferrans VJ Tomita Y Eidbo EE & Jones M (1987) “Evaluation of expanded polyurethane trileaflet cardiac valve protheses” J Thorac Cardiovasc . Surg, 94, 419-429. Kumudine C & Mark JE (1999) Mat Res Soc, 576, 331-336. Piwnica A & Westaby S (1995) Stentless Bioprostheses, ISIS Medical Media, Oxford. Rivlin RS & Thomas AG (1953) “Rupure of rubber part 1. Characteristic energy of tearing”, J Polym Sci, 10, 291-318. Tsunoda K, Busfield JJC, Davies CKL & Thomas AG (2000) Effect of materials variables on the tear behaviour of a non-crystalizing elastomer” J Mat Sci, 35, 5187-5198.

CHAPTER 13

Using FEA Techniques to Predict Fatigue Failure in Elastomers JJC Busfield and WH Ng Department of Materials, Queen Mary, University of London, UK

SYNOPSIS Elastomer components frequently fail in service through cumulative cyclic crack growth (fatigue) behaviour. Techniques are described that can be used to characterise this behaviour for elastomers using a fracture mechanics approach where a measure of the crack growth rate is made at specific levels of stored energy release rate. These derived constitutive relationships can be applied using finite element analysis (FEA) techniques to complicated real elastomer component geometries. The energy balance technique, that is available within a typical FEA package to characterise the stored energy release rate for a wide range of components, is described. It is proposed that a realistic measure of the crack growth rate can be made from a finite element analysis that therefore allows a realistic calculation of fatigue life to be made.

1 INTRODUCTION The traditional stress versus the number of cycles to failure (S-N) approach adopted in general engineering (Callister, 1994) for determining the fatigue life of components has also been the standard approach adopted in the past by the elastomer component industry. The stress typically being the maximum principal stress measured or predicted using FEA techniques somewhere in a loaded component. With elastomer components, the results obtained from this approach would be specific to the particular specimen geometry and loading conditions, which may not be representative of the typical service conditions for the part. Therefore, it is not possible to derive specific materials data in order to calculate the failure of any general component geometry. In addition, long testing times would be required to obtain the S-N data for a wide range of geometries and the scatter in the measured results can be large. In real design and development projects, it is frequently observed that the S-N prediction and measured fatigue lives can differ by factors in excess of three orders of magnitude. An alternative technique for predicting the fatigue life of elastomer test pieces, which utilises a fracture mechanics based approach is adopted here. Lake (1995) 179

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reviewed the basic approach, whereby the energy required to drive the crack at a given rate is defined as the stored energy release rate which is also sometimes known as the tearing energy, T,

(1) where U is the stored energy, A is the area of a single fracture surface of the crack and the derivative is evaluated under conditions of constant deformation of the component or testpiece. Rivlin and Thomas (1953) showed that the relationship between crack growth rate and the tearing energy was a material property, which was independent of loading mode and specimen geometry. Similarly it has been shown by Lindley and Thomas (1963) that a characteristic crack growth rate per cycle relationship exists for an elastomer that is dependent only on the maximum stored energy release rate attained during the loading cycle. In the past, the actual stored energy release rate against applied loading relationships have been difficult to calculate accurately for anything other than the simplest components, so for these more complex types of component investigators have resorted to approximate relationships for the stored energy release rate. For example, Lindley and Stevenson (1982) used an approximate fracture mechanics approach to predict the fatigue behaviour of engineering mounts loaded in compression. Even so estimates of fatigue lives that were of the correct order of magnitude were made. This technique for predicting fatigue failure has been dramatically extended by the advent of large deformation finite element analysis. It is now possible to calculate the stored energy release rate for specific loading configurations for cracks in any component geometry. Gent and Wang (1993) successfully adopted this type of FEA approach to investigate the crack growth behaviour of bonded elastomer suspension components subjected to a large shear and were able to predict the stored energy release rate and hence the mode of failure for these types of component. Here this approach is further examined by using a FEA based fracture mechanics approach to examine fracture problems with more complex three-dimensional geometries. The technique is used to calculate the relationship between the stored energy release rate and crack size for a given cyclic fatigue loading. Reference can then be made to crack growth rate versus stored energy release rate relationships, thus allowing estimates of component lifetimes to be made. It is seen in Figure 1, taken from Lake (1983), that the crack growth behaviour, characterised using crack growth rate per cycle dc/dn versus stored energy release rate data T, as determined using pure shear tests, could be described by different mathematical expressions in different regions of crack growth rate. The current work has concentrated on studying the relationship in the engineering fatigue regime for crack growth rates that would lead to catastrophic component failure in the range of 104 to 107 cycles. In this region, shown as Region III in Figure 1, a power law relationship is seen to describe the behaviour well,

(2)

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Fig. 1 A typical double logarithmic plot of crack growth rate per cycle (dc/dn) against stored energy release rate (T) for a filled NR elastomer taken from Lake (1983). The figure is clearly divided into 4 regions each of which clearly exhibits different tear behaviour.

where X and Ψ are elastomer crack growth parameters determined from cyclic crack growth tests conducted using a pure shear test piece (Busfield, 1997). For most vulcanisates the value of Ψ lies between 1 and 6. The actual value depends largely upon the type of elastomer, for example the power exponent for natural rubber (NR) is approximately 2 and for non strain-crystallising elastomers such as styrene butadiene rubber (SBR) the value Ψ is more commonly in the region of 4 (Lake and Lindley, 1965). Next, the stored energy release rate for a component containing a crack of a specific size and orientation subjected to specific cyclic deformation was calculated. For most cracks it is likely that, as the flaw increases in size, geometric effects in the region of the crack will alter the magnitude of the stored energy release rate. Thus, the relationship between the crack length, c, and the magnitude of the stored energy release rate T must be calculated using either an analytical or finite element based technique.

(3) By combining Equations (2) and (3) to eliminate T it is possible to derive a single functional relationship between cyclic crack growth rate and the size of the flaw,

(4)

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This equation can be rearranged and integrated to predict the number of cycles to failure, Nf ,

(5) Using this approach it is possible to calculate the crack growth rates for a range of crack sizes and also estimate the fatigue life of a real component. This approach is demonstrated here for simple geometries, and some of the difficulties that need to be overcome to permit the widespread application of the technique are discussed.

2 MATERIAL BEHAVIOUR In order to use a finite element model that incorporates a model of a small flaw, it is necessary to characterise the elastomer material properties appropriately. This was a non-trivial task as the stored energy function adopted must be capable of handling the large strains that occur in the finite element models at the tip of the crack. A second complication arises from the cyclic stress softening effect, whereby during the cyclic fatigue process the materials behaviour becomes progressively less stiff from cycle to cycle. Approaches that can be used to take into account these complications are discussed in Busfield (2001). For this work, which concentrates upon the techniques that are required to model the energy release rate in elastomer components using finite element analysis, these complications are not considered. Here, the neo-Hookean constitutive law (Treloar, 1975) was adopted for simplicity, although in making this choice some aspects of the material non-linearity are ignored. For the neo-Hookean law the stored energy function, W is given as,

(6) where I1 is the first strain invariant represented by the sum of the squares of the principal stretches.

(7) and G is the shear modulus for the material. The parameters X and Ψ used in Equation (2) are determined from the cyclic crack growth rate results obtained by Ratsimba (2000) using pure shear test pieces (Figure 2). This material was a semi-EV cured, 49pphr (49 parts per hundred weight of polymer) N330 carbon black filled natural rubber material. The figure is plotted on logarithmic scales as is typical. It is seen that, for the crack growth rates of interest, the data can be fitted using the power law relationship in Equation (2) with fitting parameters in this specific case of X=2.34x10-18 and Ψ=2.90.


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Fig. 2 Experimentally derived crack growth behaviour for a N330 carbon black filled (49pphr) semi-EV NR material. Data taken from Ratsimba (2000).

3 USING FEA TO CALCULATE THE STORED ENERGY RELEASE RATE Issues relating to the choice of geometric representation of the test piece geometry as well as the type of element that is most appropriate for the finite element analysis model have been discussed in the past by Busfield (1999). Three different approaches, an energy balance, a J-integral and a crack tip closure technique can be adopted to calculate the strain energy release rate. Busfield (1996) showed that all three techniques produced equivalent results even for the complex case of a three dimensional model of the trouser tear test piece. Therefore, the actual technique selected is determined by ease of implementation for the specific problem being tackled. In this work the energy balance technique is adopted. With this approach the difference in the magnitude of the internal stored energy (δU) is calculated between two models held at a fixed displacement where the crack area A is extended by a small amount (δA). The stored energy release rate is equal to δU/δA. This approach is also sometimes known as the node release or the virtual crack extension technique. ABAQUS Standard was used for all the analysis undertaken in this work.

4 AN EDGE CRACK IN A TENSILE TEST PIECE A similar approach to that adopted here has been demonstrated (Gent, 1964 and Busfield, 2001) for the cyclic crack growth of an edge crack in a tensile test piece. Greensmith (1963) observed that the stored energy release rate relationship for an edge cut in a tensile test piece was given as,

(8)

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The actual functional relation between K(λ) and the extension ratio λ has been derived by Busfield (2001) using a FEA model of the test piece. Once this is known it is possible to substitute Equation (8) into Equation (2) and derive the relationship between the crack growth per cycle to the strain energy density in the bulk of the rubber (W) when the load is at maximum, the crack length and the material crack growth parameters thus,

(9) Following the procedure outlined in the introduction this relationship can be integrated to produce the following fracture mechanics expression that can be used to predict the fatigue life, within the power law stored energy release rate regime for a edge-crack test piece, thus,

(10) Here c0 is the initial edge-crack length, Nf is the number of cycles required to fatigue fail the test specimen and it has been assumed that Ψ is significantly greater than 1 and that the crack length at failure is much greater than c0. This technique had been used in the past by Gent (1964) to reliably predict the fatigue failure from small razor blade cuts in unfilled natural rubber tensile test specimens. Busfield (2001) has also shown that this approach also works well for predicting the crack growth in both cut and uncut tensile test pieces made from carbon black filled natural rubber.

5 CRACK GROWTH IN A REAL DOUBLE BONDED COMPONENT The next stage involved making models of real components that are known (Choi & Roland, 1996) to contain small flaws throughout the rubber which are fatigued using a range of loading amplitudes and configurations. The component selected for this analysis work was a standard compression mount, manufactured by Trelleborg, which is shown as a cut away CAE (computer aided engineering) model in Figure 3. The part is subjected to complex loading in service that can be any combination of tension, compression and shear. For the purpose of this chapter, only simple tension and simple compression were considered. The amount that the part is deformed is expressed as the ratio, ε, of the amount of displacement in either tension or compression divided by the initial undeformed height of the rubber section of the part. The stored energy release rate in this work was calculated again using the energy balance approach, where the energy reduction was monitored whilst the length of specific cracks were increased in the finite element analysis model, whilst the displacement of the metal plates was held fixed. This was done for a wide range of different values of ε for several different initial crack locations. Some of the crack locations used in this work are identified in the deformed finite element analysis plots that are also shown in Figure 3. This model is more complex than those that have been examined in the past, as the compression


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Fig. 3 The simple double bonded component examined in this investigation and the various different crack locations investigated using the finite element analysis techniques. (Note that for M2, M3 and M4 left-right symmetry has been reversed. For M1 an end plate with enlarged diameter is shown.)

mode requires crack closure to be considered together with any associated contact. At larger deformations compression also requires any geometric instability that may be encountered to be considered. 5.1 COMPARISON BETWEEN A 2D FEA MODEL AND A 3D FEA MODEL

The first crack examined is a central penny shaped crack deformed in tension. (Crack location M5 – in Figure 3 and shown again as a 3D model in Figure 4) This was examined to allow a comparison to be made between a two-dimensional axi-symmetric model as well as a half symmetry 3D model. Both of these models were relatively straightforward to analyse, as the tension mode results in only simple crack opening. The models were both used to investigate the crack behaviour for a range of displacements and for a range of range of crack lengths. The results of both analysis models are plotted in Figure 5 as the stored energy release rate versus crack length for a range of different tensile extensions, ε. The results from the 2D model are shown as the data points and the results from the 3D model are shown as the solid lines. Clearly, there is good correlation between the two sets of results. This shows that, whenever the constraints of symmetry permit that a two dimensional model should be adopted as it produces the same results with a significantly reduced computational effort. For the remaining models when the crack and the loading are symmetric a two-dimensional model was adopted. It was noted that an approximately linear relationship existed between the stored energy release rate and the crack length at any specific deformation

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Fig. 4 A finite element analysis model of the double bonded component containing an internal crack opened up in tension.

level. Thus, the crack growth rate would be expected to increase dramatically according to the power relation given in Equation (2) as the crack size increased. 5.2 MODELLING COMPRESSION OF THE COMPONENT AND THE EFFECTS OF CRACK CLOSURE

This same central penny shaped crack located at the centre of the component (M5) was also modelled in compression to see if the inclusion of such a flaw would release any energy. This required the contact between the two surfaces of the crack to be incorporated into the finite element analysis model. As anticipated no energy was released when measured using the energy balance technique. However, when measured using the JIntegral method widely varying values for the stored energy release rate were obtained for different integral contours. It was thought that these unexpected results were obtained due to the limitations of the J-integral technique when calculating the stored energy release rate for a crack profile that had closed up. Thus, the energy balance approach was adopted as the most suitable technique for calculating the stored energy release rate in this work. 5.3 MODELLING OF TENSION AND COMPRESSION FOR A RANGE OF DIFFERENT INITIAL CRACK LOCATIONS

The initial flaw could occur in a range of other locations in the model; to select the one most likely to lead to a fatigue failure required investigation. As Busfield (2001) has noted the typical inherent flaw size in a carbon black filled elastomer is about 100µm. Therefore, initial small flaws of approximately this size have to be modelled in order to develop the entire history of the crack growth behaviour from the inherent flaw size up to the final catastrophic failure crack size. One possible site for a possible crack location was at the sharp corner where the metallic end plates were moulded into the rubber profile. A crack growing horizontally and in the same direction as the end plate is referred to here as M3 and a similar crack that grows at an angle of 45° below the horizontal is referred to as M2. Both crack locations are shown in Figure 3. The finite element analysis results for the


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tension of crack M3 and M2 are shown in Figures 6 and 7 respectively. Both crack locations offer broadly similar results with the crack opening up and releasing roughly equivalent amounts of energy in tension. However, it has to be noted that the amount of energy released even at large extensions was small. If you look at the plot in Figure 1, you can see that below a certain tearing energy designated as T0 zero cyclic crack growth takes place. For the types of carbon black filled natural rubber and SBR compounds that are used widely in engineering practice, Tsunoda (2002) have showed that the size of T0 is seen to be typically around 50 Jm-2 and so tearing energies below this value are unlikely to result in cyclic crack growth. Provided that the bond was not poor, it was unlikely that any flaw greater than 200µm would exist and therefore for applied strains of less than 30% in tension it was thought highly unlikely that M2 or M3 would be the site of any crack that would result in eventual failure. Both the M2 and M3 crack locations were also modelled in compression. The results in compression were again quite similar for the two crack directions and are plotted in Figure 8 for the initially horizontal M2 crack. It was observed that the stored energy release rate decreased as the crack length increased. Therefore, an increase in the flaw size resulted in the crack moving away from the highly stressed region at the sharp corner of the metal plate into a less highly stressed region of the rubber. As this happened the stored energy release rate was reduced to a value below that of T0 for the material for all the deformations modelled in this work. 5.4 THE SIGNIFICANCE OF THE RUBBER PROFILE AT THE END PLATES ON THE CRACK GROWTH BEHAVIOUR

It appears that the technique of wrapping the rubber around the end plate, even though it contains a sharp corner is good design practice as the energy release rate in this location is too small to result in a crack growth failure under normal loading conditions. To investigate this hypothesis a slightly different crack profile was modelled as case M1. Here the metal end plates were assumed to have a larger diameter than the rubber profile. A sample of the geometry is shown as M1 in Figure 3. The results for this crack location, which originated close to the bond from the outer edge, are shown in Figures 9 and 10 for the cases of compression and tension respectively. These figures are very interesting as both exhibit what we shall refer to as a stored energy release well. For both tension and compression the amount of energy released initially decreases as the crack grows. However, in both tension and compression this trend is reversed as the crack gets to a length of about 3mm. Above this crack length the stored energy release rate increases significantly with crack length. This is because the crack is now long enough to start releasing the larger stresses that are present within the bulk of the model. However, for the crack to get through the stored energy release well the deformation has to be great enough to cause the stored energy release rate to always be greater than the T0 value of about 50Jm-2 for the elastomer. In this case a linear interpolation indicates that the deformation would have to be more than 22% in compression and 25% in tension. Below these values it is possible that quite large cracks could appear on the surface of the component none of which would eventually result in the catastrophic failure of the part as the crack growth would be eventually arrested once the energy release dropped below the T 0 value. It is also interesting to note that the energy release rate from this extended end plate model is about 10 times greater than that from the model of a similar crack in the actual component. The effect of wrapping the rubber around the metal end pieces would clearly result in a significant increase in the fatigue resistance for this geometry.

T(Jm-2)


T(Jm-2)

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c(mm)

c(mm)

Fig. 6 Stored energy release rate (T) versus crack length (c) for crack M3 for a range of different tensile extensions.

T(Jm-2)

T(Jm-2)

Fig. 5 Stored energy release rate (T) versus crack length (c) for crack M5 for a range of different tensile extensions. The points are calculated from a 2D model the lines using the 3D model.

c(mm) Fig. 7 Stored energy release rate (T) versus crack length (c) for crack M2 for a range of different tensile extensions.

c(mm) Fig. 8 Stored energy release rate (T) versus crack length (c) for crack M2 for a range of different compressions.

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T(Jm-2)

T(Jm-2)


c(mm)

c(mm)

Fig. 10 Stored energy release rate (T) versus crack length (c) for crack M1 for a range of different tensile extensions.

T(Jm-2)

T(Jm-2)

Fig. 9 Stored energy release rate (T) versus crack length (c) for crack M1 for a range of different compressions.

c(mm)

Fig. 11 Stored energy release rate (T) versus crack length (c) for crack M4 for a range of different compressions.

c(mm) Fig. 12 Stored energy release rate (T) versus crack length (c) for crack M4 for a range of different tensile extensions.

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5.5 INVESTIGATIONS INTO THE INSTABILITY OF A CRACK PROFILE AT LARGE DEFORMATIONS

It is quite clear that the part will perform better in compression than in tension, as the crack faces are not normally opened up. The possibility was considered that a potential crack location existed that, should the part be deformed to a significant strain level, might result in the profile becoming unstable and that the crack might change into a position whereby the crack actually opened up. One potential location for this type of behaviour was thought to be at the edge of the component in the central plane of the part. This was investigated using the model shown in Figure 3 as M4. However, the finite element analysis model was not able to go beyond the point of instability where the compression was sufficient to lead to the crack opening. It was clear from Figure 11 and that in compression this crack location hardly released any energy at all at the compression levels that were attained in the finite element analysis model. However, in tension the energy release rate was quite substantial. 5.6 PREDICTING THE FATIGUE LIFE FOR A CRACK GROWING FROM THE WORST CRACK LOCATION

From this work it was apparent that cyclic crack growth should originate from small inherent flaws in the centre of the test piece geometry (M5), as this is the mode that releases the stored energy at a maximum rate for any given displacement. In compression the component would have to be deformed to compression ratios that are larger than that currently achieved in the finite element analysis models to get values of energy release rate that are significantly larger than T0 and that would eventually result in the fatigue failure of the part. The finite element analysis is limited by the large mesh distortions that are found in the regions near the modelled crack tip. The technique to calculate the number of fatigue cycles is demonstrated in Figure 13. Here, the results predicted in tension for crack location M5 at a given loading level (ε = 0.54) for a range of crack lengths are taken from Figure 5. The values of T are converted by algebraic manipulation into values of dn/dc by the use of Equation (2) using the crack growth coefficients derived by Ratsimba (2000). The area under the graph represents the number of cycles that are required to for the crack to grow from one crack length to another. For example the number of cycles required to grow from an inherent flaw size of 0.1mm to 3mm in length is approximately 4 500 000 cycles. Initial single cycle tear measurements indicate that the mode of failure has been correctly identified in tension. Experimentally measured fatigue test results for this test piece geometry compared with the fatigue crack growth predicted using the techniques outlined in this chapter are also discussed by Papadopoulos (2003) who initiated a crack in position M4 (Figure 3) by a razor blade cut. Papadopoulos et al found that the number of cycles required for a crack to grow from one length (c1) to another could be predicted to within a factor of 2. Crack growth prediction was most accurate for c1 ≥ 4mm. [It is known that crack growth rate is initially more rapid following initiation by a cut (Thomas, 1958; Lake & Lindley, 1964).] 5.7 OTHER ASPECTS OF CRACK GROWTH BEHAVIOUR THAT REQUIRE FURTHER INVESTIGATION

Other problems that still have to be overcome to make the technique generally applicable to a wide range of problems include:

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Log10 dn/dc(m-1)


c(m) Fig. 13 Log10 of the reciprocal of crack growth rate per cycle (dn/dc(m-1)) versus crack length (c) for a tensile extension of 0.54 for crack location M1. The integral of this function determines the number of cycles to failure for a specified geometry.

(i)

Tackling the coalescing of various micro-voids, as most fatigue problems do not result from the crack growth of a single flaw. (ii) Representing the large deformations at the crack tip frequently make the FEA model unstable at strains that are lower than the actual strains that the component is subjected to. This requires time consuming mesh rezoning to be undertaken. This process should be greatly facilitated by the arrival of automatic mesh refinement. (iii) Crack growth direction has to be assumed prior to the creation of the finite element analysis model. Again automatic mesh refinement could permit the mesh to change to follow the crack growth profile. (iv) Strain induced material anisotropy such as that described by Busfield et al (1997) can lead to substantial weakening of the elastomer subjected to complex stress fields. This biaxial behaviour might have to be considered in a detailed failure analysis.

6 CONCLUSIONS Previous studies (Busfield, 2001) have shown that a fracture mechanics approach can predict the fatigue life for a carbon black filled elastomer material within the ‘power law’ stored energy release rate region to a very accurate level. These predictions of fatigue life should be significantly more reliable than was possible using a traditional SN approach. Here the work is extended to investigate the ability of a finite element analysis technique to calculate the stored energy release rate for a real component

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subjected to a range of different loading levels in tension and compression. It appears that the technique of using the energy balance to calculate the stored energy release rate is the most reliable, with the J-integral giving erratic values for flaws that close up in the analysis model. The fatigue life of a real component can be calculated by investigating how the stored energy release rate varies with crack length at specified peak cyclic deformations. This data can then be combined with the measured crack growth rate per cycle relation given in Equation (2) to derive the relation between the crack length and the number of fatigue cycles. This relation can be integrated to predict the fatigue life of the component. The results presented here and elsewhere (Papadopoulos et al, 2003) indicate that this technique could be further developed to predict the actual fatigue failure of real components subjected to a complex loading sequence of varying strain amplitudes.

ACKNOWLEDGEMENTS Both authors would like to thank Trelleborg Automotive Europe for the supply of the components and materials required for this work. One of the authors, Wei Hann Ng, would also like to thank the Malaysian Rubber Board for their financial support throughout his research.

REFERENCES Busfield JJC, Davies CKL & Thomas AG (1996) “Aspects of fracture in rubber components” Progress in Rubber and Plastics Technology, 12, 191-207. Busfield JJC, Ratsimba CHH & Thomas AG (1997) “Crack growth and strain induced anisotropy in carbon black filled natural rubber” Journal of Natural Rubber Research, 12, 131-141. Busfield JJC, Ratsimba CHH & Thomas AG (1999) “Crack growth and predicting failure under complex loading in carbon black filled elastomers” in Finite Element Analysis of Elastomers, D Boast & VA Coveney (eds) Professional Engineering Publishing, London, 235-250. Busfield JJC, Thomas AG & Ngah MF (1999) “Application of fracture mechanics for the fatigue life prediction of carbon black filled elastomers” in Constitutive Models for Rubber, A Dorfmann & AH Muhr (eds), Balkema, Rotterdam, 249-256. Busfield JJC (2001) “Using FEA techniques to predict failure in elastomers” International Rubber Conference, Rubber Division of the Institute of Materials, Birmingham, UK,12-14 June. Callister WD (1994) An introduction to materials science and engineering 3rd Edition, John Wiley and Sons, New York, 203-206. Choi IS & Roland CM (1996) “Intrinsic defects and the failure properties of cis-1,4-polyisoprenes” Rubber Chem Technol, 69, 591-599. Gent AN & Wang C (1993) “Strain energy release rates for crack growth in an elastic cylinder subjected to axial shear” Rubber Chem Technol, 66, 712-732. Gent AN, Lindley PB & Thomas AG (1964) “Cut growth and fatigue of rubbers. I. The relationship between cut growth and fatigue” Applied Polymer Science, 8, 455-466. Greensmith HW (1963) “Rupture of rubber X. The change in stored energy on making a small cut in a test piece held in simple extension” Applied Polymer Science, 7, pp 993-1002.


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Lake GJ & Lindley PB (1964) “Cut growth and fatigue of rubbers. II. Experiments on a noncrystallizing rubber” Applied Polymer Science, 8, 707-721. Lake GJ & Lindley PB (1965) “The mechanical fatigue limit for rubber and the role of ozone in dynamic cut growth of rubber” Applied Polymer Science, 9, 1233-1251. Lake GJ (1983) “Aspects of fatigue and fracture of rubber” Progress of Rubber Technology, 45, 89-143. Lake GJ (1995) “Fatigue and fracture of elastomers” Rubber Chem Technol, 68, 435-460. Lindley PB & Stevenson A (1982) “Fatigue resistance of natural rubber in compression” Rubber Chem Technol, 55, 337-351. Lindley PB & Thomas AG (1963) “Fundamental study of the fatigue of rubbers” Proc Fourth Rubber Technology Conference, IRI. TH Messenger (ed), London, 1-14. Papadopoulos IC, Liang H, Busfield JJC & Thomas AG (2003) “Predicting cyclic fatigue crack growth using finite element analysis techniques applied to three-dimensional elastomeric components” in Constitutive Models for Rubber III, JJC Busfield & A Muhr (eds), Balkema, Rotterdam, 33-39. Ratsimba CHH (2000) “Fatigue crack growth of carbon black reinforced elastomers” PhD Thesis: Queen Mary, University of London Rivlin RS & Thomas AG (1953) “Rupture of rubber. Part 1. Characteristic energy for tearing” Polymer Science, 10, 291-318. Thomas AG (1958) “Rupture of rubber. V. Cut growth in natural rubber vulcanisates” Polymer Science, 31, 467-480. Treloar LRG (1975) The Physics of Rubber Elasticity, 3rd Edition, Clarendon Press, Oxford. Tsunoda K, Busfield JJC Davies CKL & Thomas AG (2002) “Contributions to time dependent and cyclic crack growth to the crack growth behaviour of non strain crystallising elastomers” Rubber Chem Technol, 75, 643-656.

CHAPTER 14

Fatigue Life Investigation in the Design Process of Metacone Rubber Springs W Wu, P Cook, R Luo and W Mortel Trelleborg Industrial AVS, Leicester, UK

SYNOPSIS A case study is reported on the design of a Metacone mounting used as a primary spring fitted at the wheel axle box on a railway vehicle. In use the rubber layers are loaded in shear and compression and the Metacone mounting provides controlled complicance along three axes. Requirements for increased service life and dimensional limitations (implying high strain levels) have led to an ever closer focus on suspension spring design. (In the current example the general space envelope was 250mm in diameter by 250mm high.) Furthermore, as was the case here, end of life is often defined in terms of clearly noticeable cracks or changes in stiffness rather than final failure. The location, formation and early stage development of fatigue cracks are therefore key issues in such cases. Design methods involving finite element (FE) and fatigue life analysis (FLA) were used to redesign the Metacone. As a result the life of the Metacone undergoing customer-specified (single axis) fatigue testing was increased more than ten-fold.

1 INTRODUCTION Trelleborg Industrial AVS is a world leader in the design and manufacture of rubber to metal bonded components for anti-vibration applications and suspension systems used in rail, marine, industrial and civil engineering applications. Over many years of design and application experience, our products have fulfilled the service lives required by customers with very few fatigue failure problems. Here we examine the example of a Metacone mounting (rubber spring) design. A potential problem that can occur when striving to achieve today’s high performance and service life requirements is investigated and it is shown how such problems can be overcome using finite element analysis (FEA) techniques and engineering know-how. Large Metacones are used in rail applications as primary suspension springs or as a component of secondary suspension springs (see Figure 1). When used as primary springs they are fitted, singly or in pairs, between the bogie frame and axle box. When axial (2 direction) load is applied to the Metacone, the rubber layer is loaded with 195

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Fig. 1 Schematic showing the location of Metacone mountings (dark grey) used in rail applications as primary suspension springs (i.e. directly above the axles).

Fig. 2 Diagram of Metacone (rubber shown as dark grey). The 2 axis (axial direction) is an axis of cylindrical symmetry. The space envelope of the mounting was 250mm diameter by 250mm high.

combination of shear and compression (see Figure 2). In the rail vehicle application, the Metacone can provide axial, horizontal (longitudinal and lateral), torsional and conical movement for vehicle bogie. Since the axial movement is dominant, only axial displacement is studied in this chapter.

Fatigue Life Investigation in the Design Process of Metacone Rubber Springs

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Space envelope constraints lead to very high strains in addition to more demanding service life and anti-vibration requirements (Figure 2). The combination of these requirements has led designers to focus on suspension spring design more closely now than they have in the past. Damage leading to failure of rubber components is often promoted by mechanical cycling, chemical degradation, and elevated temperatures. Lake GJ & Thomas AG (1988), Lindley PB (1972), Busfield et al (1999) and others (Suresh, 1998) have made significant contributions to understanding rubber failure and/or have provided reviews of work in this area of knowledge. Here we focus on the damage due to mechanical effects in a normal air environment at normal ambient temperatures. Specifically, we address the question of prediction of fatigue life of a new Metacone design – without prior knowledge of where fatigue cracks might first appear.

2 CASE STUDY Initial design prototypes of a 2 layer Metacone had been produced for a new rail bogie. The Metacone design was based on standard in-house criteria for strength and fatigue to fulfil customer-specified stiffness, loads and fatigue life requirements. A fatigue life of 4.8 x 106 at 2 Hz cycles of 40 to 72kN was required for the Metacone. (End of useful life was defined as either the formation of clearly apparent cracks or as a clearly apparent drop in stiffness, whichever occurred sooner.) However, when fatigue tests were performed it was found that large splits occurred in the upper and lower free surfaces of the inner rubber layer after only about 0.5 x 106 cycles (see Figures 3 and 4). The goal was therefore to re-design the Metacone so as to give the required stiffness and fatigue life but without additional manufacturing cost. The design had to be accomplished in a very limited time, as full fatigue testing of the new bogie was imminent. Design options, within the specified space envelope, were reviewed. The review process included finite element analysis (FEA) modelling of options. Adjustments were made to

Fig. 3 Metacone (initial design) after approximately 500 000 cycles of 40 to 72 kN axial loads. (Upper surfaces shown with component under load.)

Fig. 4 Metacone (initial design) after approximately 500 000 cycles of 40 to 72 kN axial loading. (Lower surfaces shown with component under load.)

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material constants used within the (Mooney-Rivlin) material model, based on the quasistatic (axial) force-deformation curve. Design parameters were revised so as to achieve (as indicated by FEA) a more uniform distribution of strain energy density within the component and so [in line with a fatigue life prediction method – Equation (3) and following] as to lessen tensile stresses at the free surface of the rubber. A fatigue test was performed on a Metacone of revised design. 2.1 FINITE ELEMENT MODEL

As indicated above, finite element analysis has been used to analyse the stress distributions and evaluate the fatigue behaviour. Taking advantage of axial symmetry in geometry and loading, an axi-symmetric model with approximately 4000 degrees of freedom was used. The meshes for the (unloaded and loaded) finite element model are shown in Figures 5 and 6 respectively. The analyses were conducted using the general-purpose nonlinear finite element code ABAQUS Standard on a HP UNIX parallel CPU workstation. In order to predict stiffness and stress distributions etc, it is necessary to arrive at appropriate material models and failure criteria. There are several hyperelastic material models that are commonly used to describe rubber and other elastomeric materials based on strain energy potential or strain energy density (U also often written as W, Gough et al, 1999). The strain energy potential can be expressed by the following (compressible, Rivlin) polynomial series:

(1) Where Cij and Di are temperature dependent material parameters, Jel is the elastic – – volume strain, I 1 and I 2 are the (“volume-neutralised”) strain invariants (Gough et al, 1999). If only the C10, C01 and D1 coefficients are non-zero, Equation (1) simplifies to the (compressible) Mooney-Rivlin material law (found to be appropriate for modelling rubbery materials if they are not highly filled and provided that the strains are not excessive):

(2) An FE model of the Metacone was developed using the Mooney-Rivlin constitutive law. Meshes of the model, which had about 4000 degrees of freedom, are shown in Figures 5 and 6. The material constants in Equation (2) were obtained from previously established empirical databases of a similar rubber material. The material properties used are associated with a moderately filled (nominal 55 IRHD) synthetic polyisoprene with good low creep performance. These were adjusted based on comparisons between the axial (2-direction) quasi-static force-deformation curve for the Metacone given by experiment and the curve given by the FE model. The (FE derived) plot of axial force against axial displacement is shown in Figure 7. It can been seen to be very similar to the experimental plot for the Metacone, giving some confidence that the material constants could be used to derive stresses, strains etc to be used in fatigue life predictions.


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Fig. 5 Undeformed mesh used in the finite element model for the Metacone Mounting. The boundary conditions are that the outside surface is fixed, 2-direction (axial direction) loading is applied to the inner metal and there is no relative movement between metal and rubber in outer surface.

Fig. 6 Mesh for the finite element model of the Metacone after the application of maximum nominal design load to the inner surface in the downwards direction (negative 2-direction).

2.2 FATIGUE LIFE PREDICTION METHOD

In parallel with the test programme (see below) a fatigue life prediction method was developed. The life estimation method was based on previously-obtained data for the rubber material used and on an effective stress (σf) . σf was a function of the principal Cauchy stress ranges.


L [%]

200

E [%]

Fig. 7 Plots of (axial) Metacone load (normalised by maximum fatigue load and expressed as a percentage, L) against deformation (normalised to maximum fatigue deflection and expressed as a percentage, d). Measured and (FE) calculated results are shown.

Fig. 8 FE-derived plots of strain energy (normalised by total strain energy and expressed as a percentage, E) of inner and outer Metacone sections against overall deformation of Metacone [normalised by maximum fatigue (axial) deflection and expressed as a percentage, d].


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(3) Here σ1, σ2, σ3, are, for each of the principal stresses, magnitudes of the stress “ranges” (differences between maximum and minimum values); A and B are weightings and the following assumptions are made. a. There is no fatigue damage when a point is under compression in all directions. b. A (or B) is taken as positive when σ2 (or σ3) is positive (i.e. tensile). c. The fatigue damage caused by any one of the other two principal directions will not exceed that caused by σ1. A number of procedures to give A and B are under consideration. In one of the procedures, at a free surface A (or B) is given the maximum value (unity) for safety, provided that σ2 (or σ3)> 0 and the value 0 if σ2 (or σ3 ) ≤ 0. That is

(4)

(5) d, the normal vector to the crack plane, is predicted via the following procedure. Let the three principal stress “ranges” be

Then ≤

(6a)

(6b) where

(7)

(8)

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(9)

(10)

2.3 FAILURE ANALYSIS (INITIAL DESIGN)

As stated above, the product had large splits in the upper and lower rubber surfaces of the inner layer but there was not any sign of failure in the outer layer (Figures 3 and 4). It was observed that the outer rubber layer was stiffer than the inner layer, which underwent larger strains when the component was subjected to deformation in the 2 direction (axial direction). Strain energy densities were calculated by finite element analysis (FEA). Curves comparing strain energy (for the inner and outer layers) are shown in Figure 8. The results indicated that at a given Metacone deformation the total strain energy stored in the outer layer was only 61% of that stored in the inner layer. Because the volume of the inner layer was 72% of the outer it follows that the average strain energy density was much higher in the inner layer. Figure 9 shows the strain energy density distribution (U) in the rubber with the maximum axial fatigue load applied. Regions of high strain energy density occur (a) [highest] at the fold on the inner upper rubber-air surface, (b) near the junction of the inner lower rubber-air surface with the intermediate metal layer and (c) at the innermost rubber-metal interface. Figure 10 shows a plot of maximum principal stress. (Again the maximum axial fatigue load had been applied.) In addition to regions (a)-(c) (above) moderately high maximum principal stresses occur near the midway circumference of the inner upper rubber-air surface. However, despite these measures being commonly used in design for fatigue, neither high strain energy densities nor high principal stresses appear to correlate well with the location of fatigue cracks in this case. Rather the highest strain energy densities and maximum principal stresses occurred in the area of rubber surface folding – not where fatigue cracks were observed. (Previous experience has shown that folding does not necessarily contribute to failure; the results here support this view.) The fact that the higher average energy density occurs in the inner rubber layer, rather than the outer does seem to be related to the appearance of fatigue cracks there. At the free surface of the inner rubber layer the highest tensile stresses there did appear to coincide with the appearance of the fatigue cracks. [Because of the particular geometry and symmetry in this case the locations of the highest tensile stresses tangential to the free rubber surface are also locations of highest horizontal stresses (σ11 or ) as shown in Figure 11.] The fatigue life prediction method based on the approach shown above [Equations (3)(10)] gave a maximum value of 1.24MPa for σf – occuring near the observed locations of fatigue cracking. S-N curve data (generated from testpieces of similar material) predicted


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Fig. 9 Strain energy density (SENER, U or W) distribution (kJ/L) plot at maximum fatigue (axial) load in the rubber for initial Metacone design.

Fig. 10 Maximum principal (Cauchy) stress distribution (S, maximum principal, MPa) at maximum fatigue (axial) load in the rubber. (Initial Metacone design.)

Fig. 11 Horizontal (radial) stress distribution (σ11 or S11, MPa) at maximum fatigue (axial) load for initial Metacone design.

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that fatigue cracking would occur at 300 000 cycles in the Metacone – in reasonable agreement with the observed behaviour. 2.4 REVISED DESIGN

With the knowledge of the fatigue failure in the existing part, new geometries of Metacone were proposed and were modelled with the same mesh densities. In each case the tensile strains and stresses in the critical areas were carefully examined. The new design selected for physical testing had a good balance of average strain energy density between the rubber layers and optimised rubber air-surface profiles to minimise tensile surface stress without changing the stiffness or exceeding the design space envelope. FE calculations were again performed to indicate that the correct stiffness would be achieved and to indicate the stresses etc. Compared with the initial design there was a 58% reduction in maximum strain energy density. The maximum principal stresses and the tensile strain at the free surface of the rubber inner layer were reduced to less than half in the revised design (see Figures 12 to 14), although they were still tensile stresses in the rubber surface at maximum (fatigue) load. [For the revised design the maximum horizontal stress (i.e. σ11 or S11) was no longer in the inner rubber layer.] The maximum tensile stress σ1 in the free surface was now calculated to be below 0.8 MPa. According to the finite element predicted stresses and S-N data from rubber testpieces the fatigue life was predicted to be around 5 million cycles as required. A new Metacone was manufactured to the revised design using new mould profiles

Fig. 12 Strain energy density (SENER, U or W) distribution (kJ/L) at maximum fatigue (axial) load for revised Metacone design.


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Fig. 13 Maximum principal (Cauchy) stress distribution (S, maximum principal, MPa) at maximum fatigue (axial) load for revised Metacone design

Fig. 14 Horizontal (radial) stress distribution (σ11 or S11, MPa) at maximum fatigue (axial) load for revised Metacone design.

and a new metal interleaf. The outer and inner metal parts of the original design were recovered and used again without modification due to time constraints. 2.5 RESULTS

Fatigue tests were carried out on the revised product. The requirement of 4.8 million fatigue cycles was achieved without any cracks appearing (Figure 15). Moreover the stiffness reduction over the test was only 7% (Figure 16). The fatigue life had increased by

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Fig. 15 Metacone (revised design) after approximately 4.8 x 106 cycles of 40 to 72 kN of axial loading. (Upper surfaces shown.)

Fig. 16 Plots of measured (axial) load (normalised by maximum fatigue load and expressed as a percentage, L) against deformation [normalised by total displacement and expressed as a percentage, d]. Plots before and after 4.8 x 106 fatigue cycles are shown for revised Metacone.

an order of magnitude or more. In addition, the result was consistent with the (σf -based) fatigue life prediction method. 3 CONCLUSIONS Using Trelleborg’s rubber engineering experience and prediction methods based on FEA, Metacone designs have been compared side by side and evaluated for fatigue life – where end of useful life is defined here as the appearance of clearly noticeable cracks or a clearly apparent drop in stiffness. It has been found that very considerable improvements in fatigue life can be achieved. In this application, prediction of the location of the fatigue cracks was important and


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challenging. Although the stresses in the air surface of the rubber may appear low they can have a very significant effect on the development of cracks. Conversely, high stresses or strain energy densities within crease areas will not necessarily cause failure. Within the constraints of the project the design methods adopted appear to have been successful – although limitations in time and cost precluded exhaustive testing of the methods and designs considered. However the general approach has now been applied to other Trelleborg designs with good results.

REFERENCES Lake GJ & Thomas AG (1988) “Strength properties of rubber” in Natural Science and Technology, AD Roberts (ed) Oxford University Press, Oxford. Lindley PB (1972) “Energy for crack growth in model rubber components” J Strain Analysis, 7, pp 132-140. Busfield JJC, Ratsimba CHH & Thomas AG (1999) “Crack growth and predicting failure under complex loading in filled elastomers” in Finite Element Analysis of Elastomers, D Boast & VA Coveney (eds), Professional Engineering Publishing, 235-250. Suresh S (1998) “Fatigue of Materials” Cambridge University Press. Gough J, Gregory IH & Muhr AH (1999) “Determination of constitutive equations for vulcanized rubber” in Finite Element Analysis of Elastomers, D Boast & VA Coveney (eds), Professional Engineering Publishing, 5-26. Luo RK, Wu WX, Cook PW & Mortel WJ, (2003) “Fatigue life predication and verification of rubber to metal bonded springs” in Constitutive Models for Rubber III, JJC Busfield & Alt Muhr (eds), Balkema, 55-57 Luo RK, Wu WX, Cook PW & Mortel WJ, (2004) “An approach to evaluate service life of rubber springs used in rail vehicle suspensions”, Journal of Rail and Rapid Transit, 218, 173-177.

CHAPTER 15

Fracture of Rubber-Steel Laminated Bearings AH Muhr TARRC, Brickendonbury, Hertford, UK

SYNOPSIS Design rules for laminated rubber bearings are reviewed. The load, shear and tilting capabilities are still usually assessed on the basis of estimates of local strains rather than a fracture mechanics approach. Experimental work on fatigue of laminated bearings is reviewed, showing that cracking can occur surprisingly rapidly in view of the excellent performance of such bearings in the field. The application of fracture mechanics to interpret these results is considered and found to be promising although based on linearised theory. The problem of the early stages of crack growth remains a challenge.

1 BACKGROUND Laminated steel-rubber bearings were developed in the 1950s to accommodate thermal expansion of bridge decks. They consist of a sandwich of several relatively thin layers of rubber bonded between parallel steel reinforcing plates. The relative inextensibility of the steel plates and the high bulk modulus of the rubber ensure that the stiffness in the direction normal to the plates is high and the load bearing capacity, in this direction, is adequate to support the bridge deck, while the construction preserves the low shear stiffness of the rubber in the plane of the layers, so that thermal expansion of the deck can be accommodated with minimal force. Usually the whole laminated structure, and at least the sides, is encapsulated by a rubber “cover layer”, a few mm in thickness, to provide an impermeable barrier to corrosion of the steel. The deployment of rubber-steel laminated bridge bearings has been a success. The only instances of replacement seem to have being instigated by considerations other than fatigue failure, such as upgrading the load capacity of the bridge or removal of a bearing to determine whether its properties have changed after prolonged service. In the latter cases, the answer is generally that, for natural rubber (NR) bearings, the stiffness remains close to the original specification (Ab-Malek & Stevenson, 1984; Stevenson & Price, 1986; Fuller & Roberts, 1997). Chleroprane rubber (cr) bearings can stiffen over time, because of “marching cure” (Tyler, 1988). The success of the design concept can largely be attributed to the authors of the Technical Memorandum that regulated their use in the UK, BE1/76 (Dept. of the 209

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Environment, 1976). The main design equations from this standard were carried forward to BS5400 part 9.1 (1983) and more recently to prEN1337-3 and, in a more disguised form, to AASHTO (current), Elastomeric Bearing Design Method B. One key equation that operates to limit the design displacements and vertical load is based on a limit applied to the maximum local strain in the rubber. This is estimated on the basis of linear elasticity theory for the bearing deformation behaviour. Although this approach is simplistic, experience suggests it has resulted in conservative designs. Interest in pushing laminated bearings to greater loads and deflections than normal for bridge bearings has arisen from time to time, for example in offshore oil applications (Gunderson et al, 1992) or for seismic isolation bearings (Muhr, 1996). The work presented here was stimulated by a need for a high rotation precompressed rubber laminated spring to prevent uplift of a spherical bridge bearing under dynamic loading. The assembly was being considered for a bridge having a particularly high ratio of dynamic to static loading, and a check that a satisfactory fatigue life would be achieved was required, not simply verification that the design met the standard rules. This chapter first reviews the equations for strain field and stiffness derived for laminated bearings from linear elasticity theory, then discusses how these are applied in the bridge bearing standards, and how the treatment can be extended to include fracture mechanics. The findings are discussed in the light of some fatigue results for a loaded laminated bearing in cyclic rotation. For simplicity, and because the high rotation bearings are circular, attention will be restricted to circular bearings, a geometry not originally addressed in the bridge bearing standards, although prEN1337-3 incorporates an annex on elliptical bearings.

2 BASIS OF BRIDGE BEARING DESIGN METHODOLOGY 2.1 STRAIN FIELDS IN A DEFORMED SINGLE BONDED RUBBER LAYER

Figure 1 shows a single rubber layer; it is considered that the flat faces are bonded to rigid plates and the curved surfaces are unstressed so that they can deform freely. For the purposes of this chapter the rubber will be treated as incompressible. Although corrections for compressibility, available in the literature (e.g. Lindley, 1979), are significant for high shape factors, they would obscure the argument, which in any case would remain inexact because of the assumptions of infinitesimal strain and linear stress-strain material behaviour, and the fact that the boundary conditions on the free rubber surface are not fully satisfied. The strain fields may be derived either as good guesses, compatible with displacements that satisfy the boundary conditions, leading to an upper bound for the strain energies and stiffnesses (e.g. Lindley, 1979; Muhr & Thomas, 1991), or from a pressureshear relation suggested by viscous flow of a liquid squeezed between plates (e.g. Gent & Meinecke, 1970). The latter approach suggests a reason why the results may be good approximations even when the local shears are large: in simple shear, the stress-strain relationship of rubber is nearly linear – provided that the material is not highly filled (Coveney & Muhr, 1993). The shape factor S of the layer is the ratio of one loaded face to the force free area and is given by

Fracture of Rubber-Steel Laminated Bearings

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Fig. 1 Undeformed single rubber layer, radius a, thickness h with coordinate axes defined.

(1) The shear strain field due to a compression of e = δh / h is given by (Lindley, 1979; Muhr & Thomas, 1991; Gent & Meinecke, 1970):

(2a) giving a maximum at r = a, z = h / 2 of

(2b) The shear strain field due to a tilt of θ about the y axis is given by (Gent & Meinecke, 1970):

(3a) giving a maximum at r = a, z = h / 2 of

(3b) In addition the bearing may be subjected to a simple shear deflection, resulting in a nominally uniform shear strain of magnitude

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(4) where d is the shear deflection. The basic idea behind BE1/76 was to add the local shear strain contributions given by Equations (2b), (3b) and (4) to estimate the maximum local strain in the rubber, and impose an upper permissible bound. The locus of the maximum strain is at the bond edge, as shown in Figure 2.

Fig. 2 Cross section of a bonded rubber disc subjected to combined shear, compression and tilt showing the locus of maximum shear strain.

Noting that live (that is, fluctuating) loads make a higher contribution to fatigue damage than static loads, the idea of linear superposition of strains was extended to separately quantifying maximum strains due to dead and live loadings, with a larger factor applied to the latter:

(5) where D and L denote dead and live effects respectively. prEN1337-3 takes values of 1.0 and 1.5 for kD, and kL respectively, and in addition multiplies γcomp,D and γcomp,L by 1.5 before inserting into the formula. The limit is taken as 5 in the serviceability check or 7 in the ultimate limit state. 2.2 STIFFNESSES OF A SINGLE BONDED RUBBER LAYER

The stiffnesses in the three modes of deformation may be calculated by integration of the


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total strain energy associated with the strain fields given in Equations (2) and (3) (e.g. Lindley, 1979; Muhr & Thomas, 1991), or by integrating over the corresponding pressure distribution (e.g. Gent & Meinecke, 1970). We find that the compression stiffness is given by

(6) and the tilting stiffness by

(7) Here G is the shear modulus of the rubber, M is the moment applied and θ is the rotation (tilt). To the usual good approximation, the shear stiffness is given by assuming a state of uniform simple shear

(8)

2.3 STIFFNESS OF MULTIPLE LAYER RUBBER-STEEL BEARINGS

For squat bearings with uniform layers under low-to-moderate loads the vertical and horizontal compliances of a bearing are given to a good approximation by the sum of the compliances of the individual layers. For more slender bearings and/or high loads, calculation of overall stiffness is more complex – see Thomas (1983) for example. 2.4 CRITERION FOR FAILURE OF RUBBER

Equation (5) assumes that susceptibility to fatigue correlates with maximum local strain. In fact, there is considerable evidence that fatigue cracks initiate at pre-existing flaws in the rubber, and suffer an increment in length in each load cycle that depends on the maximum value of the strain energy release rate, where the strain energy release rate T is given by

(9) where U is the total strain energy in the rubber, A is the area of one side of the fracture and the partial derivative is evaluated with a fixed boundary so that external surfaces do no work during the increment in the fracture surface (e.g. Gent et al, 1964; Yeoh, 2005).

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Elastomers and Components: Service Life Prediction – Progress and Challenges 3 FATIGUE STUDIES FROM THE LITERATURE

3.1 STUDIES OF FATIGUE IN COMPRESSION

Stevenson (1986) investigated compression fatigue of square and rectangular natural rubber (NR) bearings (S = 9.5 to 52) for stress (τc) cycles with maxima in the range 45 to 260 MPa (not quite fully relaxing). Here τc was compressive load divided by cross sectional area of sensing. Substantial crack growth, parallel to the steel plates but in the rubber, was noted after several kilocycles, as shown in Figure 3. The maximum test duration in the tests was 30 kcycles. The presence of a rubber cover layer did not offer significant protection. The crack growth rate was much as expected from a crude estimate of tearing energy

(10) — where W is the mean strain energy density in the rubber layer, estimated on the assumption of a linear load-deflection behaviour and using the analogue of Equation (6) for the compressive stiffness of rectangular bearings, with a correction for bulk compliance. Roeder et al (1990) investigated fatigue of 11 polychloroprene (CR) and 2 NR bearings in compression (and another similar set in shear, under constant compression). The bearings had shape factors between 3 and 6.4 and were cycled up to compressive stresses of 5.2 to 12.2 MPa for 254 kcycles to 2.2 Mcycles. Various minimum compressive stresses (0.8 to 5.2 MPa) and stress ranges (4.0 to 12.2 MPa) were used. Protrusion of rubber was perceptible in all cases after a few kilocycles, indicating the presence of interlaminar cracks. The greatest rates of cracking were observed for a high stress range and a low minimum stress; almost no cracking was observed for a bearing with the highest minimum load.

Fig. 3 Sketch of locus of failure of laminates after subjection to dynamic compression (Stevenson, 1986).


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3.2 STUDIES OF FATIGUE IN SHEAR

Roeder et al (1990) also investigated fatigue of bearings under constant compressive load in cyclic shear. The bearings had shape factors of 4.4 or of 5.3 and compression stresses were 3.8 to 17 MPa. They were cycled at maximum shear amplitudes (fully reversed) of 15, 50, 60 or 85% for up to 21 kcycles. In all cases protrusion of rubber was observed in less than one kcycle, except for the bearing cycled at 15% shear amplitude, which showed no sign of failure up to 20 kcycle. In all cases the shear strain amplitude was less than 6Se so that the local shear strain at the bond should not have been relaxed during the cycling. Cover layers did not seem to be particularly effective at suppressing cracking. 3.3 STUDY OF FLEXELEMENTS

Gunderson et al (1992) tested flexelements – annular rubber-steel laminated bearings with spherically curved reinforcing shells – under varying axial load and angular rotation amplitudes cycled in phase. The effect of angular rotation is to put the rubber layers into nominal simple shear. The flexelement suffering the most extreme deformations had completely failed (complete cracking through at least one rubber layer) after 0.8Mcycle; tests on another four elements under different conditions were stopped before complete failure. They were then sectioned, and substantial cracks were found in all (after 2.5Mcycles or less) except for one that was subjected to 14Mcycles at the smallest amplitudes and non-reversing conditions. A fracture mechanics interpretation of the crack growth correlated well with the observations.

4 LINEARISED FRACTURE MECHANICS INTERPRETATIONS 4.1 WELL DEVELOPED (“DEEP”) ANNULAR CRACKS

Let us assume that annular cracks of depth c have grown inwards from the edge at the bottom and top of the pad, adjacent to the bond, see Figure 4.

Fig. 4 Annular crack of depth c growing into a bonded rubber layer.

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Assume also that the cracks are relatively deep so that the effect on the stiffnesses is to replace a in the formulae by a-c, which should be a reasonable approximation if h < c 45º. The existence of a strain singularity in this region creates problems for FEA, since the finer the rubber is meshed, the larger becomes the strain. Theoretically, if the basis of Equation (17) is applicable to regions of non-uniform strain, we see that T might reach a finite limit for a crack of infinitesimal length at the location of an infinite strain energy density. Depending on the magnitude of this limit, initiation may not be inevitable at the singularity, since there is a threshold value T0 below which mechanical crack growth does not occur. Lindley & Teo (1979) found a limiting value of T of 0.4Wh in their plane strain


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Fig. 6 Fillet of rubber with bonded and free surfaces.

FEA study of cracks at the bond edge of a block in shear. It is surprising that this value scales with h, since the local conditions at the edge would not be expected to be directly dependent on the pad thickness. Although the limit holds for quite a wide range of crack lengths (0.015 < c/h < 0.1) it may be that it arises from the special case of the nonuniformity of strains near the free surface in nominal simple shear, rather than from the Adkins singularity which may only predominate for even shorter cracks. Suffice it to say that the use of low-angle fillets or radiusing of the reinforcing plates is good practice, and that quantifying initiation from flaws, by the mechanism of Section 4.2, at the bond edge is uncertain. 5 EXPERIMENTAL STUDY OF FATIGUE IN TILTING Tests were carried out (at between 1 and 2 Hz) on a particular design of rubber-steel laminated bearing being considered for an application as a precompressed spring to prevent uplift for spherical bearings. The design details are given in Table 1, for prototype half scale bearings. The scaling was applied to the linear dimensions; the tilt was not scaled since it is dimensionless, and the load was reduced by the square of the scale factor, so that stresses and strains are unchanged by the scaling. It may be shown that the maximum load condition (full vertical load plus tilt) very slightly exceeds the serviceability check limit given by inequality 5. Since it was known that the tilting of the bearings would be frequent, associated with the passage of heavy goods vehicles over the bridge, it was decided to validate the suitability of the design from a theoretical and experimental study. Prototype half scale bearings were made by Silvertown UK Ltd using a proprietary Natural Rubber (NR) formulation. The crack growth characteristics of this material were tested at TARRC using edge-cracks in tensile testpieces, giving the results shown in Figure 7. Taking these results, together with the fatigue life of dumbbells cut from the material, it is possible

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Table 1 Design parameters of the prototype bearings.

10000 y = 15.088x1.7556

dc/dn (mm/Mcycle)

1000

100

10

1 0.1

lambda = 1.27 lambda = 1.47 lambda = 2.0 lambda = 2.5 1

10

100

T (kJ/m2)

Fig. 7 Crack growth characteristics for the NR compound used for the prototype bearings (R= 0; 4.4Hz). The parameter, λ, is the extension ratio.


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to deduce the effective size of the inherent flaws (Gent et al, 1964), and an estimate of 70µm was obtained in this way. It should be noted that NR materials do not suffer from time dependent crack growth, so that no progressive cracking should occur as long as the bearing is subjected to only a static load. The cyclic crack growth rate depends not only on the maximum strain energy release rate during the cycle, but also on the minimum strain energy release rate as well. The results of Figure 7 refer to the case that the ratio R of minimum to maximum strain energy release rate in the cycle is zero. If R>0 the crack growth rate would be expected to be reduced (Lindley, 1973; Gunderson et al, 1992), and in fact for this material the effect of non-relaxing conditions was extremely marked. Figure 8 shows what happened to an edge crack after prolonged cycling under nonrelaxing conditions; the crack tip became progressively more ragged with little advance. The material seemed to have a particularly pronounced retardation in crack growth rate under non-relaxing conditions; under fully relaxing conditions this crack would have been growing at about 450mm/Mcycle. The multiple cracking of the material in the region of high strain near the crack tip is believed to be caused by a small concentration of ozone that might have been present in the laboratory. Away from the crack tip

Fig. 8 State of an edge cut (currently about 1.5mm long, not counting the multiple fine cracks) in a tensile strip after 7Mcycles under 175% strain, and non-relaxing conditions (R=0.1; frequency 4.4Hz).

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multiple lesions about 0.1mm in length, oriented normal to the tensile strain, could be discerned if the bent rubber strip was viewed in a bright light with a magnifying glass, indicative of the presence of some ozone. Table 2 gives the results of estimations of the strain energy release rate for the various load cases and crack lengths for the prototype bearings. Long crack values are estimated using Equation (16), but ignoring the effect of c on S. Short crack values are estimated using Equation (18), setting the initial crack size to be ci = 70µm.

Table 2 Estimates of shear strain extrema (γ) at the locations of the maximum strain and corresponding strain energy release rates for prototype bearings under a static average stress of 20.3MPa fatigued in tilting (Rlong is Tmax/Tmin for Tlong).

A test bearing was fatigued at the design vertical load for 40 kilocycles at the fully reversing design tilt amplitude. No incipient failure was noted. T short = 1.1 kJm -2 corresponds to an initial crack growth rate of about 0.015mm/kcycle, so we might have expected cracks to grow to about 0.6mm if conditions had been fully relaxing and the increase in tearing energy with crack size is ignored. Note, however, that according to the regression fit in Figure 7 a crack of 0.6mm long would propagate (600/70)1.76 = 47 times faster [see Equation (17 or 1)] than for one 70µm long, so that the increase in crack length cannot be ignored. On completion of 40 kcycles at the design amplitude, the tilt amplitude was doubled. After 64 further kilocycles, bulges were noted in the cover layer half way up the sides of the bearing at the locus of the maximum strains. Now Tshort ~ 3.4kJm-2 [using Equation (18) and ci = 70µm] and conditions are relaxing;


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we would expect an initial crack growth rate of about 0.1mm/kcycle. According to Equation (17) and the power law characteristic of Figure 7, this rate will rapidly increase:

(19a) We may deduce by integration that (e.g. Gent et al, 1964):

(19b)

where T i is the initial tearing energy and N is the number of cycles it takes for the crack to grow to length c. Putting values for B, β and ci of 15.1µm kcycle-1(kJm-2)-β, 1.76 and 70 µm respectively, we predict that c will have grown equal to the thickness h = 3.5mm of the rubber layer after only 0.7kcycle. At a length of this order T long would be expected to have become the appropriate value rather than Tshort. From the value Tlong = 1.2kJm-2 (Table 2), and taking conditions to be fully relaxing, the crack growth rate should stabilize at around 0.02mm/kcycle. As noted in Section 4.1, the tilting contribution taken on its own is probably about double the value (0.6kJm -2 in the present case) given by Equation (14), and, with simple addition of the contributions this would revise the values up to T long = 1.82kJm -2 giving a crack growth rate of 0.042mm/kcycle. Even higher crack growth rates would follow if we use the square of the sum of square roots combination. The overall expectation is that after the 64 kilocycles at double the design tilting amplitude a crack several mm long will have developed. Removal of the cover layer on one side confirmed that interlaminar cracking was responsible for the bulge, the maximum depth being about 7mm. The tilt amplitude was reduced to the design level; further crack growth was monitored, but it seemed to slow down and after another 80kcycles, and about 7mm more crack growth, it had apparently stopped. This is qualitatively consistent with the prediction that the cyclic conditions are non-relaxing under the design tilting amplitude. Similar results were found from fatigue tests on two other test bearings.

6 DISCUSSION The distribution of shear stresses given by Equation (2a) has been found to be in good agreement with experiment (Gent et al, 1974) as also have the stiffness equations. Therefore, despite their basis in linear theory, the equations in Sections 2.1 and 2.2 may be accepted as good approximations. For high shape factors they could be improved by allowing for the bulk compliance of the rubber (e.g. Lindley, 1979). In addition, the bearing could be treated as a beam-column that is soft in shear (Gent,

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1964); this would enable the shear and tilt to be estimated for each layer, rather than assuming with the standards that the total deformation is divided equally between the layers. In the case of the prototype bearing, application of the beam-column theory shows that the tilt across each layer increases to a maximum halfway up the bearing, where the bulge developed, whereas the shear is zero (by symmetry) at this position, and greatest at the ends. Cracking was found to be greatest in the middle two layers of the bearing, and confined to the middle14 (out of 20) layers. The experimental observations made on fatigue of the prototype bearings in tilting are in accord with the fatigue studies on bearings from the literature, reviewed in Section 3. It seems that growth of cracks from the outside edge of the reinforcing plates is unavoidable under typical compressive loads and cyclic conditions that are severe enough to result in the local shear strain passing close to, or through, zero. However, the crack growth rate would be expected to stabilise as the length approaches that of the layer thickness. For NR bearings under non-relaxing conditions the extent of fatigue cracking would be expected to be very much less. It looks as if Equation (5), derived from linear theory, might be quite useful for deciding if conditions are relaxing or non-relaxing, at least for combinations of compression loading and tilting. However, Roeder et al (1990) observed that fully reversed cyclic shear strains superimposed on static compressive loads lead to quite rapid fatigue, even though the nominal shear strain amplitude is considerably less than the calculated local shear strain 6Se [see Equation (2b)] due to compression, and hence would be expected not to result in fully relaxing conditions. This suggests that either the local total shear strain might be underestimated in combined compression and simple shear, or that the experiments were complicated by inadvertent tilting or relief of compression during the shear cycles. They also found a less marked effect of minimum load in compression fatigue than might be expected from this work and that of Gunderson et al (1992), – suggesting that the effect of non-relaxing conditions may be less marked for the elastomers, predominantly CR, used in their tests. Fatigue of laminated bearings is characterised by rapid crack initiation, because of the very high stress concentrations at the edges of the reinforcing plates, followed by progressive and non-catastrophic crack growth behaviour. Fracture mechanics has been reasonably successful at predicting the crack growth behaviour, using essentially the annular crack model of Section 4.1, which seems to work even for the very early stages of crack growth (see also Lindley & Teo, 1979, 1979 and Gunderson et al, 1992)). The behaviour is distinct from fatigue of many other rubber engineering components, for which most of the lifetime is spent before any cracks are readily observable, and, once observed, cracks grow rapidly and result in failure. The difference is accounted for by the presence of unavoidably large stress concentrations, a consequence of using thin reinforcing plates, high shape factors and very high loads. Such stress concentrations pose a challenge to the modelling of the early stages of fatigue, for example as expounded in Section 4.2 or by Mars (2005), based on the assumption that the magnitude and not the gradient of the strain energy density controls the fracture energy for growth from flaws.

7 CONCLUSIONS Laminated bearings can suffer fatigue cracking surprisingly rapidly (evident after a few kilocycles under severe, relaxing or reversed cycling) even though they usually perform very well in service. The cracks initiate at the edge of the reinforcing plates and grow inwards, into


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the rubber layers, permitting the layers to partially extrude under load, and form bulges in the cover layer where there is one. The initial stage of crack growth (or “initiation”, but believed to be controlled by the same energy release mechanism as subsequent stages) takes place quite rapidly and remains a challenge for both analytical and finite element analysis (FEA) simulation approaches, because it is associated not just with a region of high stress but also with a very high stress gradient. An energetics approach to the prediction of subsequent crack growth, based on simple analytical expressions, looks promising, and could be further refined using finite strain FEA calculations of energy release rate. In contrast to the situation with other types of rubber engineering components, for which the service life is dominated by the time for microscopic flaws to grow to a mm or so in size, slow growth of the cracks, perhaps many mm in size, through the rubber layers is more significant in the determination of service life for laminated bearings subjected to severe loading conditions. The effect could be more clearly addressed by the existing standards. In particular, whether conditions are non-relaxing or not for the local strains is expected to be very important, the rate of fatigue damage being greatly reduced under non-relaxing conditions for NR. It looks as if the existing linearised theory for the local strains will be useful for compression and tilting deformations, or their combination, but there is a concern that the contribution of shear to the local strain at the bond edge may be underestimated. Characterisation of filled NR under nonrelaxing conditions can be difficult, because it is slow and influenced by crack forking and small concentrations of ozone.

ACKNOWLEDGEMENTS The author would like to acknowledge Silvertown UK Ltd and the Civil Engineering Division of the Netherlands Ministry of Transport, Public Works and Water Management for sponsoring the study on the high rotation bearing and for permission to publish the material on it. Thanks are also due to Ashley Haines (Silvertown UK Ltd), Ing J.S. Leendertz and G.W. Heine (Netherlands Ministry of Transport), and my colleagues Julia Gough, John Kingston, Ian Stephens and Virginia Gledhill (TARRC) for technical discussions and assistance.

REFERENCES Ab-Malek K & Stevenson A 1984 “The assessment of the long term performance of rubber bridge bearings for use in highway bridges” MRPRA report for the Dept of Transport, ref BE 22/2/0127. Adkins J E (1952) BRPRA Laboratory Report, April. 1952. AASHTO (current – regularly updated) “Standard specifications for highway bridges” Elastomeric bearing design method B. BS5400:Section 9.1:1983 “Code of practice for design of bridge bearings”. Coveney VA & Muhr AH (1993) “Elastomer-based engineering products: design” in Encyclopedia of Materials Science and Engineering, RW Cahn (ed), Pergamon, 1636-1647. Department of the Environment, Highways Directorate, 1976, “Design requirements for elastomeric bridge bearings”, Technical Memorandum (Bridges) No. BE1/76. prEN1337 (2003) Structural Bearings-3 Elastomeric Bearings, June, 2003 draft. Fuller KNG & Roberts AD, (1997) “Longevity of NR structural bearings” Proc International Rubber

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Conference, Kuala Lumpur, October 1997. Gent A N (1964) “Elastic stability of rubber compression springs” J Mech Eng Sci, 6, 318-326 Gent A N, Lindley PB & Thomas A GG, (1964) “Cut growth and fatigue of Rubbers. I The relationship between cut growth and fatigue”, J Appl Polym Sci, 8, 455-466. Gent A N & Meinecke E A (1970) “Compression, bending and shear of bonded rubber blocks”Polymer Eng & Sci 10, 48-53. Gent A N, Henry R L & Roxbury M L (1974) “Interfacial stresses for bonded rubber blocks in compression and shear” J Appl Mechanics, 855-859. Gregory I H & Muhr A H, (1999) “Stiffness and fracture analysis of bonded rubber blocks in simple shear” in Finite Element FEA of Elastomers, D Boast & V A Coveney (eds), publ. Professional Engineering Publishing., London. Gunderson R H, Stevenson A, Harris J A, Gahagan P & Chilton T S (1992) “Fatigue life of tension leg platform flexelements” Proc Offshore Technology Conference, Houston, May. 1992 Haringx J A (1949) “On highly compressible helical springs and rubber rods. Part III” Phillips Res. Report, 4, 206-220. Lindley P B (1973) “Relation between hysteresis and the dynamic crack growth resistance of NR” Int J Fracture 9, 449-462. Lindley P B (1979) “Compression moduli for blocks of soft elastic material bonded to rigid end plates” J Strain Analysis 14, 11-16. Lindley P B & Teo S C (1979) “Energy for crack growth at the bonds of rubber springs” Plastics & Rubber: Materials and Applications, 4, 29-37. Malek AB & Stevenson A (1984) “The assessment of the long term performance of rubber bridge bearings for use in highway bridges” MRPRA report for the Dept of Transport, ref BE 22/2/0127. Mars W V (2005) “Heuristic approach for approximating energy release rates of small cracks under finite strain, multiaxial loading” (This Volume). Muhr A H (1996) “The deflection capacity of laminated bearings” Proc Fourth World Congress on Joints and Bearings, Sacramento, September ; publ. ACI, September. Muhr A H & Thomas AG (1991) “Geometrical factors in elastomer pad design” Proc Third World Congress on Joints and Bearings, Toronto, October; publ. ACI, October. Rivlin R S & Thomas AG (1953) “Rupture of rubber. Part I Characteristic energy for tearing” J Polym Sci, 10, 291-318. Roeder C W, Stanton J F & Taylor A W (1990) “Fatigue of steel-reinforced elastomeric bearings” J Struct Engineering, 116, 407-426. Stevenson A (1986) “Fatigue crack growth in high load capacity laminates” Rubber Chem & Technol, 59, 208-222. Stevenson A & Price A R (1986) “A case study of elastomeric bridge bearings after 20 years service” Proc Second World Congress on Joints and Bearings, Detroit,; publ. ACI. Thomas A G (1983) “The design of laminated bearings I” in Proc Int Conf on NR for Earthquake Protection (Feb 1982, KL), Derham C J (ed), publ MRRDB, Feb. Tyler S C (1988) “Which rubber for structural bearings?” Rubber Developments 41, 98-99. Yeoh O H (2005) “Strain energy release rates for some classical rubber test pieces by finite element analysis” (This Volume).

Index abrasive wear tests 113-36 apparatus 123 bi-directional 124, 135 definitions and terminology 114 force plots 127-32 image inspection and analysis 126-7 in lubricated conditions 121 material loss results 132 materials tested 123 microvibration frequencies 117-18 Schallamach pattern abrasion 118-21 smearing abrasion 122 strain energy release rate 121 and temperature 117, 121 types of abrasion 114-15 tyre abrasion 121 unidirectional 123-4, 126, 133-5 accelerated ageing tests 3-25 Arrhenius plot method 4, 6-9, 18-19 extrapolation of test results 4, 8 lifespan criteria 13 materials tested 5, 10-11 O-ring seals 146-8 test methods 9-13 agglomeration and magnetorheological devices 167 air ageing 12 annular cracks 215-17 ANSYS 80, 83, 85-7 Arrhenius plot 4, 6-9, 18-19, 52-5, 143 asymmetrical deformation of O-ring seals 146 axisymmetrical test pieces 79-80, 86-7, 95 bearings see laminated steel-rubber bearings bi-directional abrasive wear tests 124, 135 biaxiality ratio 103-4 biological heart valves 171 bonded components and corrosion 39-48 cathodic disbondment 47 cathodic protection 40 crevice corrosion 46-7 electrochemical nature of corrosion 45-6 immersion tests 43-5 metal-primer interface 45 osmosis 45 salt-spray testing 40-43 zinc phosphate pre-treatments 44-5

bridge bearings 209, 210-13 carbonyl iron 167, 168 catastrophic tearing energy 33 cathodic disbondment 47 cathodic protection 40 central cracks 78-9 chemical attacks 57 Chemosil 211 primer 44 Cilbond systems 44 circumferential shrinkage of O-ring seals 150 compressed nitrogen 149 compression modelling crack closure effects 186 and initial crack location 186-7 laminated steel-rubber bearings 214 compression relaxation 12, 16, 52 compression set 9, 14-15, 16, 18, 52, 142, 1478, 163 conventionally cured NR 33-7 corrosion see bonded components and corrosion corrosion inhibitors 154-5 crack closure effects 101-103, 186 crack growth 31, 36, 37, 76, 91-93, 180-82 initiating cracks 217-18 crack location and finite element analysis 186-7 crack nucleation approaches 92-3 crack orientation 102-3, 104-8 crack profile instability 190 cracking energy density 91, 93, 96, 97-103 linear elastic formulation 97-9 non-linear elastic formulation 99-103 crevice corrosion 46-7 crosslink breakage 28, 32, 33-4 cut growth measurements 33, 35-6 cyclic strain range 64, 67 dynamic stored energy 668 dynamic strain energy 64-5 edge cracks 78-9, 84, 183-4 efficiently cured (EV) NR 33-7 electrochemical nature of corrosion 45-6 electrorheological fluids (ERF) 166 electrorheology (ER) 165-6 elongation at break 9, 13-14, 18

231

232

Index

energetics 75 energy release rates 91-110 biaxiality ratio 103-4 crack closure 101-102 crack orientation 102-3, 104-9 cracking energy density 91, 93, 96, 97-103 linear elastic formulation 97-9 non-linear elastic formulation 99-103 heuristic estimates 96-7 multiaxial effects 103-9 small cracks under tension 93-7 stored energy release rates 179, 183 strain energy density 94-6, 97 strain energy release rates 75-88 engine mounts 27 EPDM materials 19, 21 fatigue tests 59-72 equilibrium swelling measurements 30-1, 33-4 EV (efficiently cured) NR 33-7 explosive decompression 56-7, 163 extrusion gap 154 fatigue tests 59-72, 179-92 changes in physical properties 71 and cyclic strain range 64, 67 and dynamic stored energy 68 and dynamic strain energy 64-5 filled and unfilled EPDM 65-71 methods and materials 61-3 results 63-71 stress versus number of cycles to failure 179 finite element analysis 55-6, 179-92 2D and 3D models 185-6 compression modelling 186 crack closure effects 186 crack location 186-7 crack profile instability 190 for edge cracks 183-4 fatigue life predictions 190 Mettacone rubber springs 198-9 and stored energy release rates 180, 183 strain energy release rates 75-6, 80-83 tension modelling 186-7 FKM (filled fluorocarbon elastomer) 153, 154 flexelements 215 FLEXPAC 81, 86-7 Flory-Huggins relation 31 fluid environments 154-9 fluorocarbon rubber materials 23 force plots 127-32 fracture mechanics 91-93

gas seals see O-ring seals gas-induced rupture 163 Griffith criterion 75 Haigh diagrams 60 hardness as an ageing measure 14 hardness maps 148-9 heart valves see synthetic heart valves heuristic estimates 96-7 holiday area of coatings 47 image inspection and analysis 126-7 immersion tests 43-5 initiating cracks 217-18 laminated steel-rubber bearings 209-25 annular cracks 215-17 bridge bearings 209, 210-12 compression fatigue 214 failure criterion 213 flexelements 215 initiating cracks 217-18 shear fatigue 215 stiffnesses 212-13 strain at the bond edge 218-19 strain fields 210-12 tilting fatigue 219-23 LEFM (linear elastic fracture mechanics) 91, 105, 105-7 Lord Corporation 166 lubricated abrasive wear conditions 121 magnetorheological devices 165-8 matrix materials 168 saturation magnetization 167 sedimentation and agglomeration problem 167 service life 168 matrix materials for magnetorheological devices 168 memory effects 163 metal-primer interface 45 Mettacone rubber springs 195-207 failure analysis 202-5 fatigue life prediction method 199-202 finite element analysis 198-9 strain energy density calculation 202 microvibration frequencies 117-18 multiaxial effects 103-9 nitrile O-ring seals 149 non-accelerated natural ageing tests 24-5

Index NR2 materials 13, 19 conventionally cured NR 33-7 efficiently cured (EV) NR 33-7 O-ring seals 141-50, 154 accelerated ageing experiments 146-8 Arrhenius rate law 143 asymmetrical deformation 146 circumferential shrinkage and stiffening 150 and compressed nitrogen 149 compression set 142, 147-8 explosive decompression 163 extrusion gap 154 in fluid environments 154-9 hardness maps 148-9 material properties 148-9 nitrile O-ring seals 149 physical simulation 143-6 pressure activated sealing mechanism 145 and pressure differences 149 silicone O-ring seals 149 stress relaxation 142 temperature effects on sealing force 159-63 thermal contraction 160 thermodynamic force reduction 160 see also seals offshore oil and gas industry 153-4 oil ageing 13, 19, 22-3 osmosis 45 ozone cracking 154 penny-shaped cracks 79, 80, 94 perfluoroelastomers 57 permanent set measurements 30-31, 33-4 plane strain 79, 84-5 plane stress 76-9, 83-4 polyurethane 171, 175-6 pressure activated sealing mechanism 145 pressure differences 149 ring cracks 80 rubber springs see Mettacone rubber springs salt-spray testing 40-43 saturation magnetization 167 SBR (styrene-butadiene) materials 59-73 Schallamach pattern abrasion 118-121 scission of molecular chains 28-9, 34, 37 seals 51-57 Arrhenius plot 52-5 chemical attacks 57 explosive decompression 56-7

233

finite element analysis 55-6 in offshore oil and gas industry 153-4 stress relaxation and set 52-5 temperature effects on sealing force 159-63 thermal contraction 160 thermal loading recovery 57 WLF (Williams-Landel-Ferry) equation 52-5 see also O-ring seals sedimentation and magnetorheological devices 167 service life prediction 5-6 shear fatigue 215 silicone O-ring seals 149 small cracks under tension 93-7 smearing abrasion 122 springs see Mettacone rubber springs stiffnesses of laminated steel-rubber bearings 212-13 stored energy release rates 180, 183 strain at the bond edge 218-19 strain energy density 76, 94-6, 97 and Mettacone rubber springs 202 strain energy release rates 75-88 and abrasive wear tests 121 axisymmetrical test pieces 79-81, 86-7, 95 for central cracks 78-9 for edge cracks 78-9, 83 finite element analysis 75-6, 79-83 penny-shaped cracks 79, 80, 94 plane strain 79, 84-5 plane stress 76-9, 83-4 ring cracks 80 for thick blocks 79, 84-5 for thin strips 76-9, 83-4 see also energy release rates; tearing energy concept strain fields 210-12 stress measurements, two-network theory 28-30, 33-4 stress relaxation 12, 14, 18, 52-5, 142 stress versus number of cycles to failure 179 stress-induced phenomena 153-64 in fluid environments 154-9 gas-induced rupture 163 temperature effects 159-63 styrene-butadiene (SBR) materials 59-72 swelling measurements 12, 22-3, 30-1, 33-4 synthetic heart valves 171-76 tearing energy concept 31-2, 36, 37, 172-3 catastrophic tearing energy 33 and crack propagation 76 see also strain energy release rates

234

Index

temperature and abrasive wear tests 117, 121 effects on sealing force 159-63 tensile strength 9, 14, 18 tension modelling 186-7 tension set 9, 17, 18 thermal contraction of O-ring seals 160 thermal loading recovery 57 thermo-oxidative ageing 3-25 Arrhenius plot method 4, 6-9, 18-19 lifespan criteria 13 test and operational temperatures 4 thermodynamic force reduction 160 tilting fatigue 219-23

two-network theory 27, 28-30, 32 equilibrium swelling measurements 30-1, 33-4 permanent set measurements 30-1, 33-4 stress measurements 28-30, 33-4 tyre abrasion 121 underbond corrosion see bonded components and corrosion unidirectional abrasive wear tests 123-4, 126, 133-5 water ageing 12-13, 19, 20-21 WLF (Williams-Landel-Ferry) equation 52-5 Wöhler curves 60 zinc phosphate pre-treatments 44-5

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